The Texans and the Eagles were
reportedly the first two teams to contact Winston. There's also been speculation that he could end up with the Dolphins, since they pursued him last year but were outbid by the Chiefs, he went to college there, and he would be reunited with offensive coordinator Mike Sherman.
I’d be surprised too if the Texans were willing to throw big money at him, though. FYI, the minimum for a veteran like him who will be in his eighth season is $840,000.