The Toffees are scouring the transfer market for attacking options as they look to back new manager Sean Dyche before the transfer window closes.
They have failed with a number of swoops so far and it has emerged they tried to sign former Arsenal and Chelsea striker Giroud.
According to Italian outlet Calciomercato.it, Everton offered Giroud €3.5m in wages until the end of the season along with a bonus of €2m if survival is secured.
He would then earn a salary of €8.4m next season, if Everton are in the Premier League.
Giroud though wasted little time in rejecting Everton’s proposal, which was made on Monday afternoon.
As the Frenchman had no intention of moving to Everton, the Toffees did not even get to the point of opening talks with AC Milan.
Giroud is fully committed to AC Milan and wants to help the club in Serie A and the Champions League.
The Frenchman is set to turn 37 years old in September.