The 23-year-old striker’s situation has been the source of constant speculation this summer since Rodgers replaced Kenny Dalglish as the Reds boss in May.
Newcastle were interested in bringing him back to St James’ Park, while West Ham United were reported to have had a bid accepted for the England international last week but the former Magpies striker was unwilling to move to Upton Park.
And although Rodgers admitted Carroll must compete with Fabio Borini and Luis Suárez for a place in Liverpool’s first-team, the Reds boss has been delighted with the forward’s attitude in pre-season.
“When I first came in I had a conversation with him about where I thought he was at,” said Rodgers. “I’ve got to say Andy has been terrific.
“He knows exactly where he stands. He’s like every player – he’ll have to fight for his position.
“There are not many clubs you can go to and be a guaranteed starter. I understand Andy wants to play games but he also really enjoys it here and I have had a number of conversations with him.
“So we’re just seeing how that develops but by the time the window shuts, whatever players are being speculated about, everyone has to be focused purely on being here.
“And certainly with the likes of Andy, from what I have seen, that has been the case.”
Carroll has scored 11 goals in 59 appearances for Liverpool after completing a £35m move from Newcastle to Anfield in January 2011.
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