Sterling looks set to leave Liverpool this summer, with the young winger determined to move away from Anfield, and Arsenal have emerged as potential suitors for the 20-year-old.
The Gunners are said to believe that Sterling could enhance their attacking ranks and they plan to make a bid at some point this summer.
Liverpool, though, are playing hard-ball with Sterling and they will not sell their prized youngster unless the deal is right for them.
The Reds know that Sterling's contract is not up until 2017, so they have time to negotiate a transfer that suits them.
Brendan Rodgers apparently feels that getting Gibbs and Walcott in return from Sterling would be a move which benefits all parties.
Gibbs did not see much competitive action for Arsenal towards the back end of the 2014/15 campaign, while Walcott's future at the Emirates Stadium remains uncertain.