West Ham are leaving the Boleyn Ground and will move to the Olympic Stadium next season.
Chelsea are at Stamford Bridge at the moment, but they are planning to move to a brand new stadium.
West Ham vice-chairman Brady has revealed that the Blues have made an approach to share the Olympic Stadium in 2018.
“Chelsea asked to come and have a look at our new home and I showed their people around,” the 47-year-old wrote in her football diary in The Sun (Monday, May 9 entry). “They commented it was one of the best football stadia in the world and that’s because it is.
“I have very good relations with Chelsea and, yes, they have enquired about a ground share in 2018. Any final decision on letting the Blues move in will be ours and not the London Legacy Development Corporation’s, or indeed Chelsea’s.”
West Ham are having a great season and could find themselves playing in the Europa League next season.
Moving to the Olympic Stadium is massive for the London outfit, who have already sold over 52,000 season tickets.
Slaven Bilic’s side will take on Stoke City away from home at the Britannia Stadium in the Premier League on Sunday afternoon.