Sterling ‘to ask for Liverpool exit’
The England forward has already turned down a new £100,000-a-week contract, and denied being a “money-grabber” in an interview with the BBC.
Sterling is due to meet Rodgers and Reds chief executive Ian Ayre on Friday, when he is set to tell them he wants to be sold.
The club are determined to keep the 20-year-old, whose contract ends in 2017.
Should he be made available, Manchester City remain the frontrunners for his signature but Arsenal and a number of leading European clubs have also expressed an interest.
While Liverpool insist they will not sell for any price this summer, their resolve may be tested by an offer in the region of £35m.
BBC Sport has learned Sterling raised the subject of his future with Rodgers before the 1-1 draw with Chelsea on 10 May.
Sterling – whose current contract is worth £35,000 a week – said in an interview on 1 April that he “talks about winning trophies” rather than money.
Liverpool’s last piece of silverware came in 2012, when they won the League Cup, and they have missed out on Champions League qualification for next season.
Former Reds defender and BBC Sport pundit Mark Lawrenson said Sterling had put himself “under pressure” with his comments.
Rodgers has previously said: “Liverpool are one of the superpowers of football and if the owners don’t want to sell, they don’t have to.”
Speaking on Friday, captain Steven Gerrard told Sterling to stay and play for a coach who “believes in him”.
“I think there is no-one better for him than Brendan Rodgers,” said Gerrard, who will join MLS side LA Galaxy this summer after 17 years at Anfield.
“The danger for younger players is they want it all too soon and go to another club and just become a number.”
Liverpool declined to comment.