The 26-year-old, who has previously attracted interest from Arsenal, joined the Hammers from Wigan Athletic on a free transfer in June 2012.
"Two years ago [before joining West Ham] I wanted to join a team with ambitions," Clubcall.com quotes him as saying.
"Liverpool? I can't tell you if I will be a Liverpool player next season. But I think my name is still on their wanted list.
"I don't hide it, I'm ambitious and I want to join a top-six side. I am 26 years old and it's time to take that step."
Diame has scored seven goals in 63 appearances for West Ham.