Earlier on transfer deadline day, speculation emerged which suggested that United had contacted the La Liga side over a possible deal for the Uruguay international.
According to The Sun, Godin's representative approached the Old Trafford club this week, claiming that the 32-year-old wanted to link up with the Premier League giants.
However, the report goes on to suggest that, only a few hours after United tabled a bid, Godin penned a new contract at the Wanda Metropolitano.
Subsequently, Mourinho has reportedly been led to feel that the agent merely wanted to use interest by the Red Devils as leverage to land the defender a fresh deal.
Godin was also linked with a move to Italian Serie A champions Juventus earlier in the summer.