The West Ham United midfielder is being strongly linked with a move this summer amid reports that the Senegal midfielder has a release clause in his contract.
And Diame admits that he is hoping to join a side challenging at the top of England's elite division at some point in the future.
"I don't want to stop here," Diame told French website Hat-trick.
"I still want more: Joining a club from the top six would be a dream come true."
Diame insists that he does not want to leave the Premier League and return to Spain, where he featured with Rayo Vallecano.
"The Premier League is something unique, you cannot compare it with another league," he said.
"La Liga is also a very good league, but honestly the Premier League has this little special thing which makes all the difference."
Diame joined West Ham from Wigan on a free transfer in 2012, but before moving to Upton Park he almost signed for Liverpool.
"In my head I was already in Liverpool," he revealed.
"It was next, I told everyone that I was there. It was as if one of my greatest wishes - to wear the Liverpool shirt - had been accomplished.
"One day my agent and I went to the training centre to see Kenny Dalglish, who was the coach.
"I found myself amongst photos of (Steven) Gerrard and co, all these great players. I was proud of myself.
"I arrived in the office and Dalglish said 'I can't guarantee you'll play every match but we have a lot of games to play'.
"He talked to me about the European Cup, my benefits and the pre-season trip to America. He sold me the dream!
"Unfortunately, Dalglish was fired and all negotiations stopped. I told myself that God wanted it that way and that is not a reason for me to stop work. It will happen one day."
Diame revealed that there were chances for him to move last summer amid interest from Arsenal, but he was happy to stay at West Ham, although he thinks the club did not do what they should have in terms of improving the squad.
"There were proposals last summer, I was thinking of going to Arsenal but it didn't happen so I stayed at West Ham, because I felt good here," he said.
"Plus, after this season we had had I thought the club would buy some better players.
"But it was a very bad start and we made the mistake of not recruiting.
"We went through the season with almost the same players, which is never good because the players think they already know who will be wearing the shirt.
"Also, people didn't necessarily give 100 per cent on the field, that's what got us in trouble.
"In January we didn't buy much but their presence was enough.
"Now if you didn't give 100 per cent in training, someone else will play. It was felt on the ground and we had the results."