The 25-year-old, who has enjoyed spells at Brighton and Sheffield United as well as Fenerbahce and Olympiakos, had spent part of the summer training with West Ham, however he now appears set to move to Ewood Park after recently joining up with the Rovers squad.
The Lancashire club are eager to add to their striking options after losing Leon Best to a knee ligament injury just weeks after the he signed from Newcastle.
Kean told BBC Radio Lancashire: "We've got Colin with us for a few days and we're hopeful we can do something.
"We've put in a bid and we'll see if that's accepted from his club. There will obviously be a tipping point for us where we'll have to look elsewhere.
"I don't know at this stage if we're close to that tipping point, but if they politely tell us that he's not for sale and they would rather we didn't bid, then we'll move onto somebody else."
Elsewhere Rovers look set to wrap up a deal for Sporting Lisbon midfielder Diogo Rosaldo in the next few days.
"I think we're in the last stages of trying to get the paperwork done to sign him," Kean added.
"He's an attacking midfield player with lovely balance and he sees the last pass. I think we're nearly there with that one."