The Sky Sports pundit was speaking after the Uruguayan striker publically reiterated his desire to leave Anfield on Wednesday, claiming that Liverpool had broken promises and that he "needed to be playing in the Champions League".

Thompson pointed out that Arsenal, who had a £40million bid for the player rejected last month, are not guaranteed a spot in this year's Champions League because they still need to overcome a two-legged qualifier later this month.

And the former Liverpool captain believes that if Suarez was to stay, then they would have a real chance of beating Arsene Wenger's side to a top-four finish next season.

"This is Arsenal bidding for him and Arsenal haven't even qualified yet for the Champions League," Thompson told Sky Sports News.

"Who knows what might happen? They haven't even got that yet and he's wanting to go to Arsenal for Champions League football.

"Certainly he's going to get the same media attention and the same difficulties as he's had at Liverpool, so is it going to be any different at Arsenal?

"And if Arsenal don't make another signing, which has been known, before the deadline happens at the start of September then where does that leave Arsenal?

"With Liverpool's signings, they could be challenging Arsenal for a top-four place next year. Why choose Arsenal ahead of Liverpool?"

Stay calm

Earlier this summer, Suarez cited press intrusion as one of his reasons for wanting to quit Anfield and Thompson says he would understand if he moved overseas.

He had been linked with a move to Spanish giants Real Madrid, but their new manager Carlo Ancelotti appears to have prioritised the rumoured £85 million signing of Tottenham's Gareth Bale.

And given the state of the transfer market, Thompson says he would not be happy to see Suarez join Real or Arsenal for less than £55m.

"Liverpool have handled it very well and the big thing is to stay calm over this," Thompson told Sky Sports News.

"They have Luis Suarez for another three years of his contract and they don't need to transfer him. He might throw his dummy out and he might be really upset, but [they shouldn't sell] until they get a price that he's worth.

"It's different when you've got £85million being offered for Gareth Bale. I'm quite sure if they want to go anywhere near that for Luis Suarez I think a deal could be done.

"Is he half the player of Gareth Bale? The club have played it right, but do you want to risk having an unhappy player around the place? We had it with Fernando Torres and is it going to be the same with Luis Suarez?

"I hope Liverpool stick to their guns. Pardon me, but £40m is not the worth of Luis Suarez and if it's Arsenal or anybody else it should be £50m to £55m.

"His good mate Edinson Cavani went for £55m and Suarez is better than him."