The Hammers have found themselves short of attacking options this season following an injury to record signing Andy Carroll.
The England man is yet to make an appearance since completing a big-money switch from Liverpool, with a nagging foot problem proving to be difficult to shake.
He is closing in on a return to training and a return to the first-team ranks, but a competitive comeback remains some way off.
His absence has forced West Ham boss Sam Allardyce to often operate without a recognised frontman, and goals have been in short supply as a result.
That issue is to be addressed, though, with funds set to be made available in the New Year.
Brady wrote in her column in The Sun: "The orthopaedic surgeon who is treating Andy Carroll is pleased enough with his progress that he is preparing to let Andy come home and start training.
"It will give everyone a lift, he's a big character on and off the pitch. I can tell every West Ham fan that Andy has worked incredibly hard with a difficult injury - and is desperate to start playing his part.
"After a chat with David Sullivan today they should also know that he is making plans to ensure we will not be left short up front again. David is looking to add at least one more quality striker in January."