After the summer departure of stalwart Wes Foderingham, who signed for Scottish outfit Rangers in July, the Robins are on the lookout for a new number one ahead of the upcoming season in the third tier.
Vigouroux, 21, was a regular for Liverpool's under-21 side last season after joining from Tottenham Hotspur 12 months ago.
He also spent time on loan at non-league part-timers Hyde, but struggled during a three-month spell, conceding 30 goals in 12 games as the Lancashire outfit dropped out of the Conference Premier.
However, Anfield boss Brendan Rodgers is now pushing to secure more first-team action at a greater senior standard for his promising young goalkeeper, by sending him to the third tier.
He has already made one appearance for the Robins, appearing as a trialist during the second-half of the club's pre-season defeat at the hands of West Bromwich Albion.
Despite impressing against the Wiltshire outfit's top flight opposition, he conceded two late goals as the tie ended in a 4-1 scoreline.
Following the completion of the reported loan move, Vigouroux will team up with Jordan Williams and Kevin Stewart, who will also spend the upcoming season at the County Ground.