Burnley are one of a number of clubs looking at the former England striker, from the bottom end of the Premier League and top of the Championship, after the 33-year-old proved his fitness during a short-term contract at the Madekski Stadium.
That contract has now come to an end after a 2-1 defeat at Middlesbrough on Saturday afternoon, in which Carroll put the Royals ahead, only for Chris Wilder's men to fire back.
Carroll has been on a salary of £1,000 a week after joining Reading in late November, having spent four months training alone after leaving Newcastle United in the summer.
He is thought to have come under consideration for Sean Dyche, as the Clarets look for solutions to their issues up front, with Chris Wood having joined Newcastle last week - after the Magpies triggered his transfer clause - while Ashley Barnes and Matej Vydra are not fully fit.
He is just an option, with Burnley also looking at other forwards on the continent.
But time could be of the essence with Carroll, who has a contract offer on the table at Reading.
That deal was put to Carroll a number of weeks ago, with Royals boss Veljko Paunović reportedly pessimistic he will stay at the club, given the growing interest in the 6ft 4ins frontman.