Carroll is understood to have travelled to France to undergo a medical and tie up a deal that will see him join the promotion hopefuls.
The former Newcastle, Liverpool and West Ham striker re-joined Reading last September after a successful first spell between November 2021 and January 2022.
However, the 34-year-old has less than a year left on his existing deal and looks set to try his hand on the continent.
Amiens have made a bright start to the season, registering three wins and one defeat from their opening four fixtures.
Sitting pretty in second place, Carroll could be the man to fire Les Licornes back to Ligue 1 for the first time since 2020.
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Carroll has clocked up 42 appearances for Reading across his two spells with the club, scoring 11 goals.
After starting the Royals' first two league games of the season, Carroll has not been involved in the club's last three fixtures, prompting a change of plans for both player and club.
The boyhood Newcastle fan began his career at St. James' Park before completing a shock £35million switch to Liverpool in 2013.
Carroll's most successful spell came during a six-year stint at West Ham where he scored 26 goals in 102 games.
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He earned nine caps for England during a two-year period between 2010 and 2012 and was part of the Three Lions squad for Euro 2012 in Poland and Ukraine.