The England international is understood to have choice between Crystal Palace and Bournemouth as his destination on a season-long loan.
Reports in Italy are reporting that the 27-year old star wants to move to Roma and that the two clubs are trying to agree a deal on his wages.
It is understood Wilshere and his representatives met Palace boss Alan Pardew on Tuesday afternoon and Cherries manager Eddie Howe in the evening.
Both those meetings were in London and Wilshere told Pardew and Howe he would inform the respective clubs of his decision on Wednesday morning.
But Italian giants Roma have now joined the race - making a "significant effort", according to Sky sources - to sign the England man, with Wilshere now having the option of a glamorous move abroad to consider too.
The combative midfielder agreed with the Gunners last week that he would go out to get regular games following a series of injuries and having made just one Premier League start last season.
Roma table late bid for Arsenal star WilshereShare:
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