Rovers boss Steve Kean is eager to offload Diouf, who has attracted controversy throughout his career and was recently accused of taunting QPR's Jamie Mackie as he lay on the ground with a broken leg.
A source close to Blackburn told ESPNsoccernet: "Yes, the club will listen to offers for Diouf. It's time for him to move on, for obvious reasons."
Blackburn were negotiating the purchase of 19-year-old Barcelona B striker Rochina even before they lost patience with Diouf, and are now edging closer to a £1 million deal.
A loan deal for Schalke midfielder Jermaine Jones is in place after the 29-year-old American international fell out with coach Felix Magath, and Kean has been in India meeting the club's owners to firm up transfer strategy.
"I will go in and out for a meeting in India and then back Tuesday morning," he said. "I am going there to give a progress report and to give a little bit more detail on what we hope to do at the back end of the window.
"It is ongoing on the transfer front. It has been slower than we hoped, which has been frustrating, but hopefully we can get this one pushed through and then we are on to the next.
"There was a signing that almost happened on Friday that went backwards a little bit, so if we can get that back on track, I'm confident that will happen.
"Then we can look and assess the injuries that are coming back and if they're coming back then that's fantastic; if not then we might add another one."
Blackburn have also been offered Levski Sofia's prolific 24-year-old striker Garra Dembele, who has scored 26 goals in 26 games this season and is available for £3 million.