Bruce is optimistic that Purse will sign the new deal but also stressed this latest offer is as far as the club can go on improving his current contract.
Bruce said: "I've got discussions ahead with Darren. The big thing with Darren was that he wanted to play in the Premiership and we are in the Premiership now.
"We've put another offer to him and we will wait and see what develops. Am I optimistic about Darren? Yes.
"I am not going to go into the financial details but when you put another offer to someone it usually means the salary has been increased a bit and this is an improved offer.
"We've gone as far as we possibly can on this one and we will wait and see what develops over the next couple of days.''