CLEVELAND, Ohio -- The Browns tried to trade for Chiefs quarterback Alex Smith, a league source told cleveland.com, but he's going to the Redskins instead.

Such is life for a 1-31 team.

The Chiefs have a deal in place to trade Smith to the Redskins, sources told Terez Paylor of the Kansas City Star. The deal between the Chiefs and Redskins, however, can't be compensated until the first day of the new league year in March.

It also means that Redskins quarterback Kirk Cousins will be available when free agency begins in March. Teams can begin negotiating with other teams' free agents on March 12, and sign them on March 14.

A three-time Pro Bowler, Smith was a target for new Browns GM John Dorsey, who had traded for Smith when he became GM of the Chiefs in 2013.

But the writing was on the wall earlier in the day. During an interview Tuesday on The Dan Patrick Show from the Super Bowl in Minneapolis, the 14th-year pro seemed to scoff at the notion of being traded to Cleveland.

"I haven't even thought about that," Smith said with a laugh. "They've got nowhere to go but up. 1-31 over the last 2 years just sounds amazing."

Asked by Patrick if ideally he'd like to go to a contender, he admitted he would.

"You would love to go a place that, if that's the case, if you're going somewhere, yeah, you want to go somewhere you have a chance to have success,'' he said. "I feel that (way). Wouldn't you?''

Of course, Smith -- who had a year left on his Chiefs deal at $17 million including bonuses -- didn't have full control over where he landed, but likely had some input.

The Chiefs will receive a 2018 third-round pick and cornerback Kendall Fuller on Wednesday, according to Ian Rapoport of NFL Network. Dorsey offered his former team one of the Browns two second-round picks, but the Browns didn't want to make the financial commitment the Redskins did because they have the No. 1 overall and are likely to draft a quarterback.

The Redskins will sign Smith to a four-year extension worth $94 million, including $71 million guaranteed.

The Browns have four picks in the first 35, and had plenty of ammunition to pull off a trade, but they are fighting the stigma of 0-16 and 1-31 over the past two seasons. Their picks in the second round are attractive -- No. 33 and No. 35.

"I wish I knew (where I'll be),'' Smith told Patrick in the afternoon. "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.''

And if he were in control?

"You're not going to like this answer at all,'' he said. "I love where I'm at right now. ... 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.''

But before Browns fans draw the conclusion that Cousins will come here to save the day, he stressed in interviews with Mike Florio of Profootballtalk.com and Jim Rome that his No. 1 priority is winning.

"Is money a part of it? Sure. Is it the only thing? No," Cousins told Florio. "It's about winning, and that's what I want more than anything. So I'm going to be willing to make sacrifices or do what has to be done to make sure I'm in the best possible position to win, and that's what the focus is going to be."

Cousins echoed those sentiments on The Jim Rome Show in the afternoon, hours before news of the trade agreement broke.

"Ultimately this decision going forward is about winning games,'' Cousins said. "I've had an opportunity to earn a good living playing football, so I want to go win. That can be Washington. It really can. (Winning is) what I'll be remembered for. That's what's going to matter.''

Cousins will command a large multi-year contract, believed to be somewhere between $25 million and $30 million, on the open market.

With the Browns likely to draft a quarterback No. 1 overall, they're not expected to want to make such a huge financial commitment to Cousins. But with Smith off the market, they'll now have to set their sights on another bridge quarterback who can start and win in 2018.

Possible candidates will include the Vikings' Sam Bradford and the Bengals' AJ McCarron, depending on who hits the market. But the Browns will have to find someone who wants to come here knowing that the probable No. 1 pick is being groomed to take his job.