Husband is expected to complete a move to Middlesbrough on Monday, with the Championship club reported to be paying somewhere in the region of £500,000 for the full-back.
Dickov hopes to use some of that money to keep Coppinger at the Keepmoat Stadium, as well as strengthen other areas of the squad.
Coppinger's decade-long stay with Rovers looked to be over last week following the collapse of John Ryan and Louis Tomlinson's takeover. The 33-year-old said he would be looking for another club with Doncaster not in a position to offer him a new deal after his contract expired this summer.
"There is a chance he will be rejoining us which will be fantastic for the whole club," Dickov told reporters following Sunday's 2-2 pre-season friendly draw with South Yorkshire rivals Sheffield Wednesday.
"Copps is a top, top pro. He's got a big influence around the football club and that's the sort of boost we need at the minute.
"My relationship with Copps is fantastic. We've been speaking all week. Hopefully there will be good news by Tuesday at the latest and he's one of them we hope to have good news about.
"Nothing has changed from my point of view. I've always wanted to keep Copps and hopefully we will get that done."
On Husband's move to Boro, Dickov added: "I think it's out there that Middlesbrough have made a bid that's been accepted. James is going up there on Monday to hold talks.
"I'm in a good position that if it doesn't go through then I've got James Husband. But if it does go through there might be a little bit of money coming back to us that we can try and strengthen the team with.
"Nathan (Tyson) and Cedric (Evina) were both out in Portugal with us and made a very good impression. We're looking at those two and a few more. We need two goalkeepers in, two that will be competing with each other which will push us forward.
"But a lot of the things that will happen early this week will depend on what happens with James (Husband). All the signs are that by the end of Monday James will be a Middlesbrough player."
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