The midfielder's current two-year deal expires at the end of the season and with Rovers' League One safety now assured, Welsh is looking to open negotiations over fresh terms.
"I'm captain and loving it here," he told BBC Radio Merseyside. "We're starting to win games and we're improving with every game.
"Hopefully things will get sorted in the next couple of weeks, but it all depends on who is in charge next year."
Tranmere have lost just two out of 10 games since Ronnie Moore replaced Les Parry at the start of March on a deal until the end of the season.
Welsh added: "The lads have been different class since the manager has come in. We've worked hard when we've had to and we've added a bit of quality when we've had to. Credit must go to the staff, to the club and to the fans for the position that we're in."