"We all know what Charlie did for us," Thompson told BBC Radio Lancashire.
"Hopefully we can come up with a transfer fee and financial package to suit him to come back here.
"It's ongoing with the chairman and Rangers, and it won't be through lack of trying if we don't get him.
"He was a great asset to us and was a big player for us towards the back end of the season, but he's just one of many that hopefully we can look after."
Adam scored twice in 13 appearances during his loan spell, helping Blackpool to ensure their survival in the Championship.
"He enjoyed it here and got on great with the lads, so he knows what Blackpool's all about," added Thompson.
"He needs to get out there to start playing and find a standard which he's comfortable with, although we're under no illusions other clubs will be after him."