The 21-year-old striker has interested a number of clubs during the last few weeks and City's new signings have pushed the player down the pecking order in terms of a starting role.
Holroyd had his name circulated along with those of Paul Rutherford and Mark Hughes last week, and he also turned down the chance of a trial at Bournemouth last week.
"According to the player's agent Morecambe are interested in signing Holroyd," said managing director Bob Gray.
"We haven't heard anything officially from Morecambe, but it appears that the agent is brokering the deal, and if it means that the player can earn himself regular first-team football, we certainly wouldn't stand in his way."
Holroyd attracted interest from Cambridge United boss Gary Brabin, and Stockport County boss, Jim Gannon, earlier this month.
Meanwhile, Chester are likely to end their interest in Trevor Benjamin as the striker continues to be dogged by a persistent eye infection
The 29-year-old former Leicester City forward has been on trial with the Blues, but he pulled out of last Tuesday's friendly against Carlisle United after his eye flared up during the pre-match warm-up.
Benjamin was sidelined for more than a month by the problem, which was complicated by the fact that he wears contact lenses, while he was with Hereford United last season.
After being forced to miss the Carlisle game, he returned to his home in the Kettering area with his Chester future hanging in the balance.
And former Chester transfer target Godwin Antwi has joined League One side Tranmere Rovers on loan until the beginning of January.
Tranmere have snapped up the Liverpool youngster in a loan move until January 2009.
Antwi joined the Reds in 2006 from Real Zaragoza and made an immediate impact helping the Reds to FA Youth Cup success in his debut season on Merseyside.
After loan spells at Accrington and Hartlepool over the past few seasons, Antwi joins Tranmere where he is the sixth signing for the club this summer.
Tranmere boss Ronnie Moore said that he has had his eye on Antwi for a while now: "When I heard Antwi had become available on loan I jumped at the chance of bringing him in to play right-back."
Blues boss, Simon Davies, has admitted he has made his last pre-season signing.
He said: "I'm done now as far as new signings are concerned. We have a really strong squad of players that can play in different formations and players that can adjust to situations on the pitch and I'm quite happy with what we've got.
"I think we're looking good - the lads are buzzing and they are ready for the kick-off."
- Find out why Stephen Vaughan is optimistic about City's chances this season on page 44.
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