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Manager Jay Saunders will make a serious effort to keep the striker after meeting with club directors to discuss next season.
Pigott has scored six goals in 16 appearances since joining on loan from League 2 Cambridge, playing a big part in their National League survival.
The former Charlton man is out of contract at the Abbey Stadium this summer and Stones will try to clinch a permanent deal.
Saunders said: “I’ve had a good chat with Joe. I think Joe would be keen on staying. I’d love to keep him. He’s a young lad, 23, who’s got a lot to learn yet.
“To come from a pro club, like he has, it could have been quite easy for him just to go through the motions but he’s worked as hard as anyone.
“He’s getting better all the time and I’ve enjoyed working with him.
“I think he’s someone who’d like to stay but I’m sure there’ll be a lot of interest.
“Stuart Lewis is another one. I know they’ve got a lot of interest so it’s always difficult but we’re now in a position where I can have serious chats with them.
“We’ll try our hardest but football’s a funny game. No doubt we’ll lose some