The 21-year-old, on loan with Swindon Town until the end of the season, was involved in an alleged assault during the early hours of March 12.
Jones has yet to make a senior appearance for the Reds following a succession of loan spells away from Anfield, most recently with Swindon where he has featured 30 times in all competitions.
A Gloucestershire police spokesman is quoted by the Liverpool Echo as saying: "We received a report at about 2.30am on Sunday March 12 of an assault at a nightclub in Regent St, Cheltenham.
"A 21-year-old man from the Plymouth area was arrested on suspicion of assault."
Jones has had his bail extended until May 29.