Glover, who was appointed as Ian Culverhouse’s successor last week, confirmed the club have taken up an option on Kennedy this summer and have made him an improved contract offer.
Unsurprisingly, the combative midfielder has seemingly attracted interest from elsewhere.
But Glover insists he wants Kennedy and other members of last season’s squad to stay on at Latimer Park.
“We have an option on Connor which we are taking up so anyone who would want him would have to pay heavy for him,” said Glover.
“But we have made an improved contract offer to him, we really like the lad.
“There have been other clubs interested in him but I want him to stay and I am working around the clock to try to make that happen.
“I said I wanted to keep the majority of the squad together and that remains the case.
“We have been talking but we also have to be realistic and there is always a timeline to these things and then a point at which we have to move on as a club.
“It’s very busy and we are in negotiations with three players who played in the National League last season so there is lots going on.”
The Poppies did see one significant departure this week with last season’s overall player of the year Alex Brown revealing on social media that he was leaving the club.