The England forward has been heavily linked with a move away from Anfield this summer, with former club Newcastle thought to be interested, but the Ulsterman is confident that the £35 million man can succeed with the Reds.
Rodgers told reporters: "Andy is a terrific young player. I had a brief chat with all the lads and over the next couple of weeks I'll be able to speak to them with more confidence and on a one-to-one basis.
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"There is no doubt he is a terrific talent. There has been a lot of unfair criticism aimed towards Andy.
"He is a player who can play in a number of styles and it was a wee bit unfair on him [for people] to say he couldn't fit into the way I would want to play.
"For me, your game is based on your players, the players you have. I am here to win games. We've got a number of very, very talented players in the group, of which Andy is one."Liverpool continue their pre-season preparations against Roma on Thursday morning, but are likely to be without Fabio Borini and those who represented England at Euro 2012, who only joined the squad in USA on Tuesday.
Rodgers conceded that the late-returners will be unable to feature in the team so soon after their rendezvous but hopes to get them involved as the tour goes on.
He continued: "As much as I'd like to put them into games straight away, you can't do that. Physically, it's not what you can do.
"The players who've been training for two-and-a-half weeks will play a big part in these next two games and we've got to manage the other players and get them tapped back into the physical side. We'll increase that as the days go forward. But it's great to get them back, get to work, and we can move forward from here.
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"It's going to take a bit of time for the group to be the kind of structured group we want them to be."
Fenway Park will host the clash with Roma, in what will be the first football match to take place at the home of the Boston Red Sox baseball team owned by Liverpool chiefs John Henry and Tom Werner.
The pre-season tie is part of the venue's 100th anniversary celebrations.
"It's fantastic," Rodgers enthused. "First and foremost, it's a great reward for the owners. They've invested not only money but also a lot of hard work into the club.
"For them to be able to bring their football club to their home patch here in Boston is great, and for us as sports people, to be able to play in one of the most historic and iconic sports venues in America is very special."