Blackpool chairman Karl Oyston claims the club have put an offer to Roman Bednar and are waiting to hear back from the Czech frontman.
The 29-year-old striker linked up with the Seasiders on a short-term deal in January, having been released on a free transfer by West Brom.
He is now out of contract once more and mulling over his options.
Blackpool are hoping he will agree to stay on at Bloomfield Road, despite injury preventing him from showing his true form last term.
He picked up a knee problem moments after opening his goal account for the club in a 3-3 draw with Leicester in March and was kept sidelined until making a cameo appearance off the bench in their Championship play-off final defeat to West Ham.
"We've spoken to Roman's agent and it's down to him now to decide where his future lies because he's a free agent," Oyston told the club's official website.
"I don't think we particularly saw the best of him, not through any fault of his.
"He came in and he got injured almost immediately after he popped a goal in.
"It would be nice for Roman to come along and join the club for a couple of years to see if he's as good as we all think he is, and I'm sure he is."