Veteran quarterback Alex Smith doesn’t sound thrilled about the possibility of the Kansas City Chiefs trading him to the Browns this offseason.

Still, he knows it could happen.

On Tuesday, Smith appeared on the Dan Patrick Show and was asked by Patrick if he’s open to Cleveland.

“I haven’t even thought about that,” Smith replied with a laugh.

Patrick told him to think about it, whereupon Smith said of the Browns, “I mean they’ve got nowhere to go but up. 1-31 over the last two years just sounds amazing.”

Then Patrick asked if landing with a playoff team would be ideal.

“If that’s the case, if you’re going somewhere, yeah, you want to go somewhere you have a chance to have success,” Smith said.

Not many people look at the Browns and see a great chance for immediate success. Despite the team’s stockpile of picks in April’s draft, including the Nos. 1 and 4 overall selections, and more than $100 million in salary-cap space, it faces a serious uphill battle after going 0-16 last season and 1-15 in 2016 under coach Hue Jackson.

Yet Smith, who’ll turn 34 on May 7, realizes he won’t be able to choose his destination if the Chiefs decide to ship him away.

“I wish I knew [where I’ll play next season],” he said. “Listen, I’ve got a year under contract there in Kansas City. I wish I was in control of this thing. I wish I was the one that got to be able to do this. That’s just not the reality.”

Patrick asked Smith what he would do if he were in control of the situation.

“I love where I’m at, right?” he said. “I felt like we underachieved. I feel like we, offensively last year, did some awesome things. But who knows? I’ve been playing long enough, I’ve been through this before -- the trade deal. So I’m not naive to it. This is a crazy business. A lot of crazy stuff can happen, so we’ll see.”

When new Browns General Manager John Dorsey was the new GM of the Chiefs in 2013, he traded a second-round draft pick and a conditional choice that ended up being another second-round selection to the San Francisco 49ers in exchange for Smith.

Drafted first overall by the 49ers in 2005, Smith has gone 50-26 as a starter in his five seasons with the Chiefs, leading them to the playoffs four times and making the Pro Bowl in each of the last two years. He’s also coming off the best statistical season of his career. He completed 67.5 percent of his passes for 4,042 yards and 26 touchdowns with five interceptions for an NFL-best rating of 104.7 in 2017.

But in last year’s draft, the Chiefs traded up from No. 27 overall, leapfrogged the Browns at No. 12 and took quarterback Patrick Mahomes at No. 10. So the passing of the torch from Smith to Mahomes is inevitable. It’s just a matter of when it’ll happen.

Smith is scheduled to make $17 million in salary and bonuses in 2018, the final season of his contract with the Chiefs. Should the Browns trade for him, they obviously would need to sell him on their plan for a turnaround if they wanted to sign him to a contract extension. Otherwise, he would amount to a one-year rental.

Jackson said last week at the Senior Bowl he wants the Browns to acquire a veteran quarterback with wins on his resume this offseason. They entered the 2017 season with no regular-season victories among their quarterbacks -- DeShone Kizer, Kevin Hogan and Cody Kessler -- and finished winless.

“Do we want to be in that situation again? No, we don’t. You need to have a quarterback that knows how to win in the National Football League, but circumstances sometimes dictate otherwise,” Jackson said. “You just don’t know how things will unfold, but if we had the best of all of the worlds, we would want a guy in there who has won in the National Football League and knows what that looks like and what that position has to play like to have that.”

Jackson said acquiring a big-name veteran quarterback and also drafting a QB at No. 1 overall is in play.

“I think all of those things are on the table,” Jackson said. “I think you discuss all of those things and you work through all of those things as you go through this.”

Smith has the track record Jackson wants, and his connection to Dorsey shouldn’t be dismissed. Earlier this month, NFL Network reported the Chiefs are open to trading Smith. Perhaps a second-round pick and a middle-round selection would be in the ballpark of what they would seek as compensation. Trades cannot become official until 4 p.m. March 14.

That’s when free agency will begin, too, and Washington’s Kirk Cousins is the top quarterback scheduled to hit the open market. The Browns could certainly afford the minimum of $26 million a year Cousins is expected to command, but he seems to be a less realistic option for them than Smith and others. Washington could use a franchise or transition tag on Cousins, and if he becomes a free agent, he may not feel compelled to resurrect an 0-16 team with other suitors pursuing him.

If the Browns were to trade for Smith, they would still likely draft a quarterback first overall on April 26. Most draft analysts consider Southern California’s Sam Darnold and UCLA’s Josh Rosen the favorites with some deeming Oklahoma’s Baker Mayfield and Wyoming’s Josh Allen candidates as well.

Nate Ulrich can be reached at nulrich@thebeaconjournal.com. Read the Browns blog at www.ohio.com/browns. Follow him on Twitter at www.twitter.com/NateUlrichABJ and on Facebook www.facebook.com/abj.sports.