The former Reds forward also believes that his old side will fall short in their quest to finish inside the top four.
The striker enjoyed an impressive start to his Liverpool career after joining from Chelsea, going on to form a deadly partnership with Luis Suarez as they finished as runners-up in the Premier League the season before last.
However, he spent the majority of last season on the treatment table with a series of injury setbacks, and has missed the beginning of the 2015/16 campaign after undergoing surgery.
Bellamy says it is imperative that Liverpool rid him of these struggles, as he is essential to their cause, although he believes both Christian Benteke and Philippe Coutinho will also be of vital importance to Brendan Rodgers in the months to come.
“They’re desperate for [Daniel] Sturridge to have an injury-free season as he holds a lot of the keys as to how Liverpool will do,” he told the Daily Mail.
“I think [Christian] Benteke is a brilliant signing – he’s definitely a player who is going to do well. For me though the star man at the moment is Philippe Coutinho – everything goes through him at the moment. For Benteke and Sturridge to have good seasons, a lot is going to have come from Coutinho.”
No top four chances for Liverpool
The former Wales international has also admitted that he doesn’t believe Liverpool will end up finishing in the top four come the end of the season.
Rodgers has been busy adding to his squad this summer, with a number of fresh faces drafted in - such as the aforementioned Benteke - as he overhauled his squad and took aim on the Champions League places.
The Reds have had a decent start as well, although a 3-0 loss to West Ham United at Anfield last time out has tempered expectations, and Bellamy is expecting them to fall just short of their ultimate goal.
“I’d love to say they can qualify for the Champions League but I feel they will fall a little bit short of that again this year,” he added.
“I don’t see it being a season like it was two years ago and I don’t think they will be too far away from the Champions League either but I think unfortunately they will just miss out on this season.”