The Robins have been unsuccessful in their approach for the Stoke City striker.
Sunderland sold Stephane Sessegnon to West Bromwich Albion back in 2013.
The striker is out of contract at the end of the season.
Bullard had earlier tipped Leicester to be in relegation trouble.
Manchester United could only manage a 3-3 draw with Newcastle on Tuesday.
Watford and Manchester City have been linked with Liverpool’s Sinclair.
Celtic’s Tom Rogic has been linked with a move to Leeds United.
The Newcastle United defender made an impressive stop on Wayne Rooney.
Lucas said he believed he was waving goodbye to fans the last time the Reds faced Arsenal.
West Bromwich albion have reportedly made a bid for a free-scoring defensive midfielder who has six caps for Senegal.