The player has been heavily linked with Arsenal as well, according to the Sun.
The Brazilian international has struggled for regular game time under Pep Guardiola and he needs to leave in order to play more often.
The Premier League champions have recently signed Erling Haaland and Julian Alvarez to boost their striking options.
Jesus is likely to fall further down the pecking order and the Brazilian needs to join a club where he can play regularly.
Real Madrid could certainly use more depth and quality in the attacking department and Jesus could prove to be an excellent signing for them.
The Spanish giants have been overly reliant on Karim Benzema for goals and Jesus could be an understudy to the French international.
Furthermore the Brazilian international can operate anywhere across the front three and his versatility will be an added bonus for Carlo Ancelotti.
Real Madrid managed to win the Spanish league and the Champions League this past season and they will be hoping to build on their success next year as well.
It is no secret that the Spanish outfit will have to improve their squad in order to keep challenging at the highest level and signing players like Jesus will certainly help them do so.
Meanwhile, Atletico Madrid have parted ways with experienced striker Luis Suarez and Jesus could be his replacement at the Wanda Metropolitano.
It remains to be seen whether Brazilian ends up eventually.