Partick Thistle manager Alan Archibald says he will not wait long for his out-of-contract players to follow David Amoo's example by agreeing a new deal.
Amoo, the 25-year-old winger who arrived from Carlisle United last summer, has signed a new one-year deal.
Midfielders Stuart Bannigan and Steven Lawless are free agents this summer.
"We will not hang about forever for them," Archibald said. "If something comes up and we need to move, we will move."
Lawless was also wanted by Dundee United, but the Tannadice club will be relegated to the Championship at the end of the season.
Meanwhile, Osman rejected Caley Thistle's advances and signed a new contract at Firhill.
"The players are wise enough to know that, in football, if they get something better, they will take it and, if we get something better, we will take it," said Archibald.
"I've not had a chat with Steven for a few weeks. His wife is due to give birth. Stevie is always a bit relaxed on that. He knows we want to keep him."
Englishman Amoo, who began his career with Liverpool before spells with MK Dons, Hull City, Bury, Preston North End and Tranmere Rovers, has made 39 appearances for Thistle.
"David's had a great second half to the season," said Archibald. "David is honest enough to admit he took a long time to settle in and get going, but we saw the best of him in the second half of the season and we've said to him he has got to go and kick on.
"He has given a few full-backs tough tough games in the second half of the season, so we need more of the same from him.
"He has given us a bit of pace and creativity and popped up with five goals.
"Now he knows the Scottish game and knows what is expected of him from ourselves, we are hoping for more from him next season."
Meanwhile, Osman (knee), defender Callum Booth (foot) and forward Christie Elliott (groin) and have undergone surgery ahead of their final Premiership match of the season against Hamilton Academical.
"We are hoping they are all going to be back for pre-season, whether it's the first day or not," added Archibald.