The Doncaster Rovers striker has been out of action with an ankle injury since the win over Barnet on October 8.
But he will take a significant step towards his return next week as he joins in with first team training.
“He’s been out on the grass,” boss Darren Ferguson told The Star.
“He did a session on Monday and Tuesday. He had a bit of rest off his feet on Wednesday then he’ll be doing sessions on Thursday and Friday.
“He’ll have a bit more rest over the weekend because he’s been out a while.
“Then he’ll train Monday.”
Ferguson hopes to have the striker fit to face Stevenage on December 3 but may choose to ease him back into action in the Checkatrade Trophy clash with Blackpool three days later.
Also taking part in light training alongside Williams is midfielder Harry Middleton who has been out since the FA Cup defeat at Oldham Athletic earlier this month.
Middleton is also set to return to full training next Monday.
Ferguson said: “Harry felt his groin against Oldham in the FA Cup. He just tweaked it a little bit, nothing serious.
“He and Andy have been working alongside each other and if they come through this week ok, they’ll train on Monday.”
Ferguson confirmed Aston Villa loanee Riccardo Calder missed the win over Hartlepool United at the weekend due to illness.
He said: “He was poorly. He picked up a bug early last week then seemed to be okay but reported on Thursday that he was quite bad.
“Friday was the same and then Saturday, he was going to start on the bench, so to sit in the freezing cold, it’s hard enough as it is.
“And I didn’t want him to pass it on to anyone else so it was a simple case of him staying away.
“But he’s okay and he was back in training on Monday.”
n Grimsby Town could be backed by more than 3,000 fans when they visit the Keepmoat Stadium later this month.
The Mariners have been allocated 3,051 tickets ahead of the League Two meeting between the sides on Saturday, December 17 (12.30pm).