Midfielders Tomas Rosicky and Mikel Arteta are also back in training.
The Hammers beat Liverpool 2-0 at the weekend to move within touching distance of the top four.
Judge has been sensational for the Bees this season.
The midfielder joined the Gers at the very start of the January transfer window.
With Villa looking certain to drop down to the Championship, manager Remi Garde should resist the urge to spend in January and give these young players a chance to show their worth instead.
The draw at the weekend extended Steve Evans' side's unbeaten run.
A selection of the latest stories in the media involving Liverpool Football Club this Tuesday morning.
Ian Wright has looked back on his time alongside Dele Alli at MK Dons.
The winger completed a £3.75m move to Premier League high-flyers Leicester City.
The Sky Sports pundit believes Stoke City will beat Liverpool in the first leg of their semi-final, while backing Everton to overcome Manchester City.
Credit Suisse has announced that it has appointed Koichi Ito as Managing Director, Head of Investment Banking and Capital Markets for Japan, to spearhead the growth of the bank’s investment banking activities in Japan.
Alexandria cuisine arrives in West London
Tottenham Under-21 coach Ugo Ehiogu has praised Andros Townsend.