Sterling missed training on Wednesday and Thursday this week after phoning in sick, following media reports the 20-year-old is reluctant to travel for matches in Asia and Australia.
The England international, who has a contract at Anfield until 2017, turned down an offer of a new deal in January and has been linked with a move to Premier League rivals Manchester City, who have reportedly had two previous bids turned down.
But Gerrard, who made 710 appearances for Liverpool before joining LA Galaxy at the end of last season, is critical of Sterling's behaviour and believes he should hold talks over his future with manager Brendan Rodgers.
"I'm not happy with all that carry-on and I don't think there's any need for it. They all need to be men about the situation," Gerrard told Sky Sports.
"Raheem needs to go in and speak to the owners and to Brendan himself, tell them what he wants and go about it that way. You don't have to throw illnesses in and refuse to go on tour."
Sterling's relationship with the club took a hit in April when he denied being a "money-grabber" in an interview with the BBC, claiming he was motivated purely by ambition.
However, Sterling's agent Aidy Ward fuelled the fire in May by saying the England winger would not sign a new deal at Anfield -- even for 900,000 pounds ($1.39 million) a week.
Gerrard, who is expected to make his LA Galaxy debut this weekend, said Sterling's relationship with the Liverpool fans would have been damaged in the fallout.
"There are millions and millions of Liverpool fans around the world who are itching to see Raheem Sterling in a Liverpool kit," he added.
"I don't think it's fair on them if he is behaving like that."
(Reporting By Michael Hann; Editing by John O'Brien)
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