The Reds are keen for the 18-year-old to spend the season at the League One club, who are already providing first-team football for full-back Kevin Stewart, midfielder Jordan Williams and goalkeeper Lawrence Vigouroux.
The reported move will be a first of his career for creative attacking midfielder Kent, who has impressed greatly while playing for the Reds U21 side and signed a long-term contract at Anfield in March.
He also impressed during his brief cameo appearance at the County Ground during a pre-season friendly in early August, when he arrived as a second-half substitute before posing a significant attacking threat throughout the latter stages of his side's 2-1 victory over the Robins.
Brendan Rodgers is a known fan of the club set-up at the County Ground, following comments made after Liverpool's pre-season visit to the County Ground this summer - as reported by Total Sport Swindon - which could sweeten a deal between the two sides.
A move for the 18-year-old would also link up with Brendan Rodgers' son Anton, who rescued a point for Mark Cooper's side at Bury on Saturday with a late free-kick.