The former Reds striker has told the Uruguayan to prove he has changed and started being recognised for his successes on the pitch rather than controversies off it
The Uruguayan is available for selection again and could face Manchester United in the Capital One Cup after serving a 10-game ban for biting Chelsea defender Branislav Ivanovic in April.
Suarez made no secret of his desire to leave Liverpool during the summer and Fowler feels the loyalty shown by the club should be repaid but is not expecting former Ajax man to act out again.
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"The club have stood by him, so have the Liverpool supporters, and you can see why because he is a phenomenal player and you want phenomenal players in your side.
"I know in the summer it looked like he was leaving and quite rightly Liverpool expected a bit of loyalty back off him and thankfully he is still a Liverpool player.
"I don't think he'll get many more chances but I don't think he will be doing anything remotely as silly as he has."
Fowler added that Suarez, who was also suspended for eight matches in 2011 for racially abusing Patrice Evra, must prove his worth on the pitch after Liverpool rejected two big-money bids for his services from Arsenal.
"You get players of the past who do silly and stupid things, it's not right but you do expect loyalty back," he continued.
"[I'd say] don't give anyone licence to shoot you down. Go and do the right stuff and be the player that we know you are.
"Let's start talking about Luis Suarez as one of the great players rather than the stupid things he does on the pitch."