Skuse is set to leave City, with his contract at Ashton Gate due to expire later this summer.
The news has alerted a number of clubs to Skuse's availability on a free transfer, with City resigned to losing him following their relegation to League One.
A host of Championship clubs are thought to be weighing up moves for the midfielder, but Ipswich are leading the race for his signature.
Town boss Mick McCarthy is thought to be a big admirer of Skuse and is keen to add him to his squad next season as he reshapes the side at Portman Road.
The 27-year-old, who has come through the ranks at City, has made over 300 appearances for the Robins.