West Ham have been persistently linked with the Arsenal midfielder, ever since his future at the Emirates Stadium became uncertain.
However, Allardyce feels that David Moyes may need to strengthen other areas of his squad before bringing in Wilshere.
“I’m not sure that West Ham don’t already have enough midfield players,” Allardyce said. “It’s up to David to decide that though. If he’s available on loan they’ll be a lot of clubs interested.”
Wilshere has had to make do with cup appearances for Arsenal in recent years, with Arsene Wenger persistently overlooking the England international.
Wilshere was sent out on loan last term to Bournemouth, and he has been unable to break back in to the Gunners’ first-team.
West Ham are thought to have funds available in January, as the board look to back Moyes.
West Ham are currently in 18th place in the Premier League table, and are in need of an injection of quality.
Moyes takes charge of his first West Ham match in two weekends’ time when they take on Watford at Vicarage Road.