The striker has been linked with a number of clubs in recent weeks, including Sheffield United, and appeared to wave goodbye to the home supporters at full-time in the 2-2 draw with Kilmarnock.
Motherwell battled back from two goals down to earn a deserved share of the spoils.
Borja Perez opened the scoring after 12 minutes when he spun before slamming the ball beyond Darren Randolph.
Paul Heffernan doubled Kilmarnock's lead against the run of play on 63 minutes, however Motherwell came storming back and goals from Murphy and Henrik Ojamaa put the hosts back on level-terms.
At full-time, manager Stuart McCall embraced Murphy and encouraged the fans to give him what looked to be a farewell applause.
"In the last few seasons it's been a pleasure to play with Jamie," said Lasley
"If he goes it will be with the blessing of the squad, the club and the fans - he's a given the fans some memorable moments and I'm sure he will go on to bigger and better things.
"Jamie loves the club and it's here where he was given his big chance - I don't think he would have a bad word to say about Motherwell."