The 23-year-old England international has been the subject of intense speculation ever since the new Liverpool manager hinted earlier this summer that he might not have a future at Anfield.
Carroll's situation remained unclear as he headed for North America to join up with his teammates in Boston after an extended break following the European Championship, but Werner is adamant that any decision will be down to Rodgers.
He told Sky Sports News: "The only thing I can say is we will do what's best for the club. At the moment, Andy is on the squad. He was an important member of the English team, he has got a lot of talent and we will see what happens there. Brendan is clearly the leader here, and hopefully the question will be answered shortly."
Carroll's former club Newcastle United have tested the water with a speculative bid to take the player back on loan with a view to completing a permanent transfer next year, prompting Rodgers to rule out a temporary switch to any club. West Ham United and Fulham are also monitoring the situation.
However, while Newcastle's interest is ongoing, it remains to be seen whether or not they are prepared to meet Liverpool's asking price, understood to amount to £20m.
Carroll was signed by the former Liverpool manager Kenny Dalglish, whose departure at the end of last season opened the door for Rodgers to secure one of the biggest jobs in English football.
Werner is delighted with the appointment and is backing the former Swansea City manager to make a significant impact.
"I don't think anyone could have been happy with our performance on the pitch last year, no disrespect to Kenny," Werner said. "Brendan brings a very thoughtful, modern, attacking philosophy - I think our fans will be very delighted with the attacking philosophy that he brings to Liverpool - and hopefully we will see improvement."
Werner also said that the spectacular spending which characterised Dalglish's reign is a thing of the past, and said: "This is a very financially strong organisation, LFC. We, in the past, I believe - not just in the previous season, but in the past - we have overspent for players and the results were not what we have expected ...
"I think you will see that you don't necessarily have to go out and spend £50m on one player to see success."
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