Reis will cost over £30million and has been eyed by several other Premier League clubs including Wolves.
Wolves have recently completed the signing of Reims defender Emmanuel Agbadou from Reims for £16.6m.
Teenager Reis has emerged through the R10 Academy, which is run by former Brazil international Robinho, who spent two years at Man City himself.
Reis has represented the Brazil under-16s and under-17s, captaining both sides and playing in the final of the Copa do Brasil under-17 competition.
City are in need of reinforcements after an injury-hit and underwhelming start to the season.
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Regular starters John Stones and Nathan Ake have started 12 games each in all competitions with the former one of Pep Guardiola's key players during a period of dominance at the Etihad.
talkSPORT understands Man City have also made contact with Lens over a move for defender Abdukodir Khusanov.
Uzbekistan international Khusanov, also shortlisted by Tottenham, is valued in excess of £30m by the French club.
The 20-year-old centre back has only one full season of experience in Europe's major leagues, having moved to Ligue 1 in 2023 from Belarusian side Energetik-BGU.
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Lens are currently sixth in the French top flight with the second-fewest goals conceded in the league.
Omar Marmoush - Eintracht Frankfurt's forward - is another target for Man City this transfer window.
Marmoush has scored 13 goals and assisted seven more in the Bundesliga so far this season and said to be rated at £50m.
Asked if City will make signings this month, manager Pep Guardiola recently said: "I don't know right now, it's not easy.
"It will not be easy. Maybe we sign, maybe we don't sign anyone.
"The club has to be wise. Don't do it just to do it.
"We want to add players for the situation that we have because the players have consistent injuries many times.
"Club has to do it but I'm not sure if it will be possible."