While City have spent big money in the transfer market, there is a desire for the Premier League leaders to start using players who have progressed through their youth ranks.
As it stands, Guardiola tends to use foreign clubs to give experience to his prospects, including at Spanish side Girona and Dutch outfit NAC Breda, but it appears that more youngsters could be allowed to spend time in the Championship.
According to The Mirror, Guardiola was impressed with Lee Johnson's style of play during the first leg of the EFL Cup semi-final between the teams earlier this month and could now hold discussions with his Robins counterpart in the near future.
Guardiola is unlikely to take up the potential option during January, but the link-up is said to be a possibility later in the year.
Bristol City are currently competing for promotion to the top flight, with the club sitting in fifth place in the second-tier standings.