The Anfield favourite believes that the Uruguayan striker is reaching an untenable position after being accused of biting an opponent for the third time in his career
The Uruguayan unexpectedly fired his side into the Premier League title race last season, scoring 31 goals and creating 12 assists in 33 appearances, but his hopes of a summer move to Barcelona or Real Madrid may now be under threat after he was accused of biting Italy's Giorgio Chiellini on Tuesday.
Regardless of his quality, Fowler feels that Suarez's position at the club may now be untenable, especially given the support that they have show to him after previous incidents.
"You can't defend him," the former Liverpool striker told talkSPORT. "Off the pitch he's an absolutely lovely fella. He does so much work for charity, does so much work in the community in Liverpool and I love him as a player but you cannot condone what he has done.
"When he gets on the pitch he just becomes a different person. I'm flummoxed for words. It's a real, real tough predicament most Liverpool fans are in. They love him as a player but he's continually dragging the club's name through the mud.
"It's not right, especially after how they helped him last time. They tried to rehabilitate him. I wouldn't be surprised if he went now."
Should Fifa's investigation find that Suarez did bite Chiellini in Uruguay's 1-0 World Cup victory to progress from Group D, the punishment could well be severe given his previous record at club level.
In 2010, while playing for Ajax in the Eredivisie, he bit PSV midfielder Otman Bakkal and later received a seven-game ban for his actions. He used his teeth again in 2013 when he bit Chelsea's Branislav Ivanovic in a Premier League match and was suspended for 10 matches.
The Football Association also found him guilty of racially abusing Patrice Evra in 2011 during a match between Liverpool and Manchester United.
A Fifa ban for biting Chiellini could potentially stretch to a maximum of two years.