The Corby Town boss had been hoping to have a deal in place by now to keep the former Barnsley and Grimsby Town striker at Rockingham Triangle.
But now Blue Square Bet North rivals Harrogate Town have also declared their interest in Jarman.
"To
be fair to Nathan, Harrogate are right on his doorstep and they've offered him £100 a week more than I can," said Drury.
"He'll certainly go and see what Harrogate have to say and then he'll make a decision from there.
"He's told me he's really enjoying it at Corby and from that perspective, he'd like to stay.
"But whether or not that's enough to persuade him to stop with us is another matter. I just hope that it can be.
"But he'll go and have a game with them this weekend and then he'll see how he feels after that."
Ironically, were Jarman to opt for Harrogate over Corby, it would still mean him starting the season at Rockingham Triangle as the Sulphurites are the opening-day opponents on August 14.
One man definitely not signing for the Steelmen is former Rushden & Diamonds midfielder Jamie McGuinness.
The 20-year-old, who was released by Diamonds at the end of last season, played for Corby in their 1-1 friendly draw at Northern Counties East League side Lincoln Moorlands on Tuesday night.
But Drury confirmed that the midfielder would not be part of his plans any more.
"At his stage in his career Jamie told me he needed regular first-team football and I simply couldn't guarantee him that," he said.
"It's nothing more than that and I can understand where he is coming from so it was best that he moved on and looked for another club elsewhere."