Roberts, who scored five Premier League goals last season from 15 starts, has been the subject of transfer speculation throughout the summer.
Championship side Leeds United have been linked with Roberts as a replacement for Jermaine Beckford, who has signed for Everton, along with Queens Park Rangers and West Bromwich Albion.
Rovers completed the loan signing of striker Mame Biram Diouf from Manchester United on Friday night, which will allow Allarydce to move Roberts on. Roberts did not travel to Scotland for the pre-season games against Hearts and Celtic this weekend.
He told the Lancashire Telegraph: "I think everyone knows by now we would listen to an offer for Jason. I felt leaving him behind rather than playing him and risking an injury would be the best bet this weekend."
Allardyce hopes to strengthen his squad further this week after sealing the signing of Diouf.
Asked if he was interested in Aston Villa's Nigel Reo-Coker, Allardyce said: "No. Not at all. We are trying to bring someone in before Saturday though. We have one or two irons in the fire that have emerged over the last few days, which are exciting me a little bit more but (we are) still quite a way from securing any permanent signing.''