Mount, whose contract has just one year remaining, is being discussed for a transfer to Manchester United, with a potential deal in the works over the next few weeks.
If Mount departs, Chelsea will need a replacement, and it is suggested by The Telegraph that Veiga is being considered as an option.
The 21-year-old Spaniard has had an impressive breakout season with Celta Vigo, scoring 11 goals and providing four assists in La Liga.
His progress has caught the attention of several top clubs across Europe, and the West Londoners will be aiming to secure his signature ahead of the competition.
Veiga currently has a release clause of £35 million in his contract, and Celta Vigo are reluctant to sell him for less during this summer.
Aside from Chelsea, other clubs like Arsenal, Manchester United, Real Madrid, and Barcelona have also been linked with the youngster.