The offer comes amid interest from Arsenal, and it includes a pay-rise and a longer contract term, which will take Mosquera's deal to multiple years beyond his current one that runs until 2026.
Accepting this offer would significantly improve Mosquera's position on the club's salary scale.
Valencia is starting its renewal plan by offering new contracts to several players, including Mosquera, Javi Guerra, Diego López, and César Tárrega.
In Mosquera's case, with his contract expiring in 2026, the club felt the need to act quickly due to Arsenal's interest in signing him.
The push for this new offer is led by Valencia's new chief executive, Ron Gourlay, who previously worked at Chelsea.