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The Uruguay striker has netted just seven times for Arne Slot's team this term.
Nunez's problems were compounded on Tuesday night during Liverpool's Champions League exit to Paris Saint-Germain.
The 25-year-old was brave enough to step up and take a penalty during the shootout but missed along with Curtis Jones to send PSG through.
And Defoe, who scored over 200 goals in the Premier League, has shared his view that there is no way back for Liverpool's No.9 at Anfield.
"He needs a fresh challenge, a different environment and maybe he just needs to go somewhere and find his form again in terms of goals," Defoe told Sports Mole courtesy of bet365's new Sub On, Play On product.
"[A move could make] people look at him and be like, 'okay, he's someone that can score goals' because I just feel like now, because it's gone on for so long, that I don't know if he can recover, unfortunately.
"It is frustrating though, because when you watch him play, he works so hard and he keeps going and he keeps going and he's so dynamic and quick.
He's got good movement but just that final bit that you need as a centre forward, for some reason he just hasn't got it but we've seen it - he's had it before he came to Liverpool.
"I don't know if he can recover now from it.
It's gone on for so long, it's almost like how do you recover from this now because you've missed so many chances.
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"With the chance that he missed [against Aston Villa], it was almost like, okay you can miss chances but people are looking at it thinking [about] 'can he recover from this?'"
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