Jackman had a transfer request rejected by the Cobblers last week and missed the 0-0 draw with Macclesfield with a knee injury but Stimson believes he wants to rejoin the Gills.
Stimson said: "We thought we were close with the boy Jackman, but that's been stopped at the moment and we'll be going back to see if there is any movement on that. We've gone in with a decent offer for someone of his age and for what he has left on his contract.
"All clubs will want more but I understand the boy has put a transfer request in. They may be better off taking some money and moving on. I think he's a decent player for them but I am led to believe that he doesn't really want to play in League Two. He's too good."
Northampton manager Stuart Gray said: "We have certain values of our players, be it Danny Jackman or any other member of our squad, and we won't sell for less than that.
"Fingers crossed they won't meet that valuation and he can concentrate on being a Northampton player."