The 26-year-old forward recently received the suspension for biting Branislav Ivanovic's arm during his team's 2-2 draw against Chelsea.
There have been fears at Anfield the controversial forward would walk out on English football, but it seems increasingly likely that won't happen with the club promising to help the player manage his emotions.
It is an approach fully endorsed by Rush and the Welshman, who played for Liverpool for 15 years over two spells, told the Soccer Extra Bank Holiday Special: "Luis is a lovely lad, a family man and he deserves what he gets but he's a very talented man.
"The ban was a bit harsh. But that's the sort of animal he is. If you take that out of him you lose the qualities he's got. He's been absolutely superb and without doubt the player of the year for Liverpool.
"He's let the club down with him missing so many games. But he's such a special talent. He's got to take the punishment and come back a much better person."
Suarez will miss Liverpool's remaining Premier League games this season and the opening six domestic matches of the next campaign.