The U’s turned down two bids from their npower League Two rivals earlier this summer.
But after selling forwards Mustapha Carayol and Chris Zebroski, Rovers are in need of more firepower.
The exits also mean they now have the resources to make an improved bid and reports in the West Country say Constable is still a target.
Manager Mark McGhee said: “I would like four more players before the start of the season, whether I can get four or whether we can afford four is another matter, but I still feel we are four players short of the squad I want to start the season with.”
Last month Constable, who finished as United’s top scorer last season with 11 goals, was reassured of his position in the squad by manager Chris Wilder .
The striker said at the time: “Obviously it’s nice to be told you’re wanted and on a personal level I want to be here.
“I love being at the club, this will be my fifth season here, I’ve enjoyed every minute of it and I’m glad that it has been put to bed so I can concentrate on starting the season.”