The Reds' troubled frontman admits he is flattered to be linked with the likes of Chelsea and Arsenal, but his countryman believes a move elsewhere in England is not an option
Suarez has been vocal in his desire to leave Anfield and move to Real Madrid this summer, citing unfair treatment by the British media as one of his main reasons.
But recent weeks have seen Arsenal and Chelsea linked with bids for his services, and the Uruguayan admits he is flattered by the interest of two of the Premier League's Champions League representatives.
But Poyet, who is currently unemployed following his dismissal from Brighton, believes moving elsewhere in England's top flight should not be an option for Suarez.
"If I was Suarez, I would either stay at Liverpool or leave England for good," Poyet told Uruguayan radio station Sport890. "Him going to Arsenal won't change a thing. If he wants to move, it's probably because of the way the media treats him as a Liverpool player, but that won't change if he moves to another club in England.
"If it's just for the sake of playing in the Champions League [possible Arsenal move], well, that's up to Luis to decide. But I'd be a lot more drastic: I'd stay put at Liverpool or leave England all together.
"I believe he has to be calm when making this decision. He shouldn't let emotions play a part. It has to be a decision that is well-thought and that will bring him good things for the future. Luis' numbers last season were out of this world. Liverpool, with all due respect, were a mediocre team last season, but Luis showed a great level."