Vaughan revealed that the flexible left-sided player, equally adept at full-back or centre-half, had disclosed his desire for a fresh challenge after three years at Victoria Park.
Having been starved of success over the past two years, Jackson has opted to begin pre-season with the Hammers – the club he represented for four seasons prior to joining Poppies.
And having been impressed by Jackson’s approach, Kemp confirmed that he hoped to seal the deal over the coming weeks, particularly on the back of United defender Shaun Brian’s departure to take up a firefighter’s job with the RAF.
On Jackson’s future, Vaughan told the Daily Echo: “He hasn’t made up his mind yet but he has said how he would like another challenge.
“I would be really gutted if he went but there would be no animosity because he has been loyal and first class for me. The door would always be open if things didn’t work out elsewhere.
“We are resigned to losing him and it is a bitter pill to swallow but we just have to get on with it.”
Opposite number Kemp said: “Jacko has been to both training sessions so far and has trained really well. I have been very impressed by his attitude and he would be a real asset to our team.
“Martin Warren has been in as well and both would massively improve our options. We are doing all we can to secure their services.”
Meanwhile, Vaughan said he anticipated that Poppies would hold onto the bulk of last season’s squad and would run the rule over a handful of trialists ahead of Saturday’s opening friendly at Shaftesbury Town.