The 24-year-old is available on a free transfer after seeing out his contract at Wigan this summer.
A number of clubs at home and abroad are thought to be chasing his signature, with Diame given permission to leave the Senegal squad this week to hold talks with interested clubs.
Diame has revealed he held discussions with Dalglish about a possible move to Anfield and that he was sad to see the deal fall through following the Scot's departure earlier this month.
"I met before Kenny Dalglish and we talked about next season, but God decided to finish this situation," Diame told Sky Sports News.
"It is true I was very sad in my head as I was thinking to go there, but that is OK as I think I have got other opportunities to go to another club."
Diame revealed he has received offers from Spain, France and Turkey, but that his preference is to stay in the Premier League.
"I am free and not everybody is free in this moment like a midfield player like me and that is why I have got a lot of clubs interested in me," added Diame.
"I have to be composed and make a good decision for my future. I have got some offers from Spain, from France, from Turkey, but I really want to stay in the Premier League."