Suarez has expressed his desire to leave Anfield for Champions League football but Liverpool remain determined to keep hold of their star striker.
The Merseysiders last week rejected a £40million plus £1 offer from Arsenal, and former Reds forward Neil Mellor does not expect Suarez to make the move to Emirates Stadium.
"I've got to be honest, I'll be absolutely amazed if he does go to Arsenal," Mellor told Sky Sports News Radio. "I just can't see Liverpool selling to a rival and that's what Arsenal will be this season because Liverpool will be targeting that top-four spot and hoping to finish above Arsenal."
Mellor believes Suarez owes it to Liverpool to commit himself to the club, and he has "no doubt" Brendan Rodgers' side can make the top four this season if the Uruguayan stays put.
"Frustration is a big thing for Liverpool fans at the moment because this Luis Suarez saga is rumbling on for far too long," Mellor said.
"Steven Gerrard's testimonial next week is an awakening for Luis Suarez. That's what loyalty is all about. Liverpool have stood by him time and time again because of the talent he is.
"It's time now for Suarez to say 'I'll give it one more season here at Liverpool and try to push to get into the top four'.
"You've got to go into the season with optimism, and Liverpool will be no different.
"The back end of last season gave room for optimism because the form was excellent and the form was [that of] a top-four side.
"If Suarez stays Liverpool will finish in the top four, there's no doubt in my mind. It does surprise me that Liverpool have been written off. I believe Rodgers will get it right."
You can hear Mellor's full interview, in which he also waxes lyrical about Philippe Coutinho, here.
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