HITC Sport understands from sources close to Leeds that the club are set to appoint Glover as their new head of recruitment imminently.
Glover currently holds a similar role with the Hammers, but Leeds have moved to offer him a position at Elland Road.
He is highly-regarded in footballing circles having also worked with the now departed Sam Allardyce at Blackburn Rovers and his appointment at Leeds is expected to be rubber-stamped in the next few days.
Leeds owner Massimo Cellino was keen to bring someone in as soon as possible to help manager Uwe Rosler revamp the Whites' squad ahead of next season.
His move does not come as a huge surprise given the uncertainty that has surrounded his position ever since former Everton player recruitment guru Tony Henry was brought in by West Ham co-owners David Sullivan and David Gold as director of incoming talent at Upton Park.
West Ham's player recruitment during Glover's time with Allardyce has been hit and miss.
But last summer is widely regarded as the best single transfer window for signings in the club's recent history. All nine signings contributed, some outstandingly so, throughout the season.
The likes of left-back Aaron Cresswell, who won a hat-trick of club awards including best signing after his debut season in the Premier League following his £3 million move from Championship side Ipswich Town, have been huge success stories.
Diafra Sakho, Cheikou Kouyate, Carl Jenkinson and Enner Valencia have also been big successes at Upton Park and had helped the Hammers to their best ever start to a Premier League season before they slid from fourth at Christmas to 12th by the end of the campaign.
However, with Henry already in place by then and Sullivan taking a much more active role in transfers last summer, it is unclear how much of that success was down to Glover.
Instead what he will more likely be remembered for in East London are two high profile incidents.
The first came back in 2013 when previously unheard of striker Michu was tearing up the scoring charts after his bargain £2.5 million move to Swansea City.
At the time Allardyce told the likes of the Daily Mail that he was frustrated with Glover for not telling him "You must sign this player" with regards to the Spanish forward.
Big Sam said then: "I wish he had (told him he must sign the player).
"You take your choices, but certainly on the basis of what he cost he would have been within our budget."
Then a month into last season, a report in the Daily Star claimed Allardyce was on a collision course with the West Ham board over their appointment of Henry given that he had 'his own trusted' Glover in place.
The paper even claimed Allardyce had banned Henry from the training ground so as not to undermine Glover.
Given that the former Bolton Wanderers and Newcastle United boss went on to leave the club at the end of the season, perhaps Glover's own exit was inevitable.