By Rich Parry
Arsenal have submitted two bids for the Uruguay striker, who has stated his desire to leave Anfield this summer.
Suarez, who received an eight-match suspension for racially abusing Patrice Evra in December 2011, will miss the first six games of the new season after being banned for 10 matches for biting Chelsea defender Branislav Ivanovic, and Hamann thinks it is time to cash in.
"Suarez missed 20 games over the last two seasons, he missed a quarter of the games through suspension and obviously this is something to take into account," he told Goal.
"He had all the support from the club, from the fans, he misses the first six games of the coming season then he turns around and says he wants to leave. I think it would be best for both parties to get rid of the player.
"Long term I think the club and the team will be better for it. Obviously he's done ever so well for the club, but sometimes when you lose a player like him the responsibilities are shared, it probably gives Liverpool the opportunity to bring two or three very good players in, and I think long-term the club will be better off without Suarez."
Liverpool are holding out for closer to £50m for Suarez, but Hamann believes they may have to settle for a lower amount because the player wants to leave, and also because he could face a monster ban if he seriously breaks the rules for a third successive season.
"Hopefully they get as much money as they want but sometimes you have to sacrifice two or three million if a player wants to go," he added.
"You never know with him, he's had previous, he did the same thing he did to Ivanovic when he was at Ajax, if he were to do anything this season you’re looking at a 20 or 25-game ban and that is something you also have to take into account when you value a player."
Meanwhile, the former Germany midfielder believes Pepe Reina may have contributed to his Liverpool exit.
The Spain goalkeeper claimed that the club had agreed to loan him to Napoli without informing him first, but Hamann believes the current situation is of his own making.
"I think some of what happened, him being out on loan, is down to his own remarks, to his own quotes he’s said in the past," he continued. "Yeah, I would have liked to see him stay at Liverpool but under the circumstances I understand why Liverpool brought [Simon] Mignolet in, I think they’ve found a very good goalkeeper and he will do very well for the club.
"Reina's form dipped a little bit a couple of years ago, towards the back-end of last season he picked up again and he was the player he was when he first signed, but he said publicly or to the manager that if Barcelona came calling he would like to go back to Barcelona.
"The club is in a position where... are you going to wait for Barcelona to come and then he leaves in two weeks’ time and you haven’t got a goalkeeper? The club had to cover their backs and I think in Mignolet they have signed a very good goalkeeper.
"If Pepe said he wanted to stay he probably would’ve stayed at the club and I’m not sure whether somebody else would’ve been brought in."