The 22-year-old American is reported to have a number of English suitors after being released by the Saints.
Cropper, 22, first began his professional career in England with Ipswich Town, before linking up with Southampton in the summer of 2012 following his release.
The Minnesota-native featured 24 times for the club’s Under-21s over the past three seasons, while posting nine clean sheets in the process, but never managed to make a first-team appearance and failed to even make the senior bench this term.
Nevertheless, having been informed earlier this week that his Saints contract would not be renewed, the American stopper is now reported to have a number of English suitors, with the Robins looking like the front-runners for his signature at this stage.
After claiming the League One title this season, manager Steve Cotterill is said to be on the lookout for another keeper to compete with Frank Fielding for the club’s number one job in the Championship and Cropper could be the answer to his needs.
Starting at the Toulon Tournament at present, the promising custodian has been called up to Jurgen Klinsmann’s senior squad on several occasions since August 2013 but he is still to earn his first cap.
With the likes of the soon-to-return Tim Howard, Brad Guzan, Nick Rimando, Bill Hamid, William Yarbrough and Sean Johnson all now ahead of him on the depth chart, he will have to see first-team action soon to keep himself in the picture and a move to Bristol would give him a much better chance than he had at Southampton.