Top Gamble could tackle the rescheduled Clarence House Chase at Cheltenham on Saturday.
A frozen track forced Ascot to cancel its meeting last Saturday, meaning the Grade One feature over two miles has been added to the Trials Day card at Prestbury Park.
The nine-year-old, who has won three times at Grade Two level, will also be given the option of the Hugo's Restaurant Barbados Trophy Handicap Chase on the same nine-race card.
Lee said: "Top Gamble is in the two-and-a-half-mile handicap and will also be put back in the Clarence House when that reopens.
"If the ground was only good to soft he might run in the longer race because over two miles he needs the mud to be at his best."
However, Nicky Henderson will resist the temptation of running Altior in the Clarence House.
The Seven Barrows handler tweeted: "Altior will not be entered in the Clarence House on Saturday. He's not ready and hasn't been prepared for it. Game Spirit still the plan."