The 28-year-old former Everton and Manchester City midfielder, who left Sunderland in August last year after the club's relegation to League One, made 22 appearances for Rovers last season and is one of three players currently engaged in negotiations.
A statement on the club's official website, www.rovers.co.uk, said: "Discussions are currently taking place with Craig Conway, Jack Rodwell and Ben Gladwin - and their respective representatives - regarding the possibility of extending their stays at Ewood Park.
"Under EFL regulations, as all three players are over the age of 24, they are entitled to discuss their options with other clubs."
Goalkeeper Jayson Leutwiler will be staying after the club took up the option of a one-year extension.
However, Paul Downing, Jack Doyle, Lewis Mansell, Charlie Albinson and scholars George Wilson and Kyle Connell have not been offered new contracts and will leave when their current deals expire at the end of next month.