Manchester City and Benayoun's former club West Ham have been monitoring his impact on Liverpool's hunt for honours over the past few months, while Atletico Madrid have been tracking him ever since his header stunned their city rivals at the Bernabeu at the end of February.
It is understood that, after just turning 29, he feels there is one more big pay day to come and that an offer of contract talks at Anfield would be enough to banish any thoughts of moving on.
Fight: Rafa Benitez
Benayoun is halfway through a four-year deal, and Benitez must decide whether to reward his improved form, and end uncertainty over his future, by presenting him with the long-term deal he is looking for.
Speaking on Israeli radio, Benayoun said: 'This has been the best season of my career. I have played a lot of games and scored some important goals, and I am very happy with that.
'At the moment, I am a Liverpool player, and unless something surprising happens, I will remain one. But after such a good season, I have had some offers from England and Spain. You have to give that some consideration, so there will probably be some discussions with Liverpool.
'I have had a great two years at Anfield and enjoyed every minute. I have long since accepted that, with one or two notable exceptions, there is no such thing as an automatic choice at Liverpool.
'Unless you are Steven Gerrard, you are going to sit out one or two games, but that is no problem. Stevie is exceptional, and the rest of us accept that.
'The good thing is, I have been playing more, and I hope it continues that way. To be honest, it could be Real Madrid knocking on my door, and I would still rather stay at Liverpool four more years.'
Would like him to stay - excellent squad player.