Walker will be allowed to walk out of The Den in six months' time because he has not signed professional forms. That would leave Millwall seeking compensation through a tribunal for the player who has also attracted an offer from Portsmouth.
His father believes he would benefit more from training with top class keepers at Stamford Bridge rather than waiting for his chance behind Lenny Pidgeley and fellow youngster Preston Edwards.
Lions boss Willie Donachie has urged the 6ft 5in teenager to wait for a chance at Millwall before making the leap into the big time.
He said: "Sam would stand a much better chance of having a career with us instead of fighting for a place with other big money foreign signings.
"Some Premier League players are stuck in the reserves for three years. How can that help? Playing senior games is the only way.
"But once a youngster is offered the glamour and the money of a Premier League team it becomes very attractive to them."