It is understood the Catalan giants have even flown scouts to England to keep an eye on the Gunners midfielder.
The La Liga champions are hoping to make the first move in January, with a view to completing the deal in the summer according to reports in Spain.
It is understood that Barcelona view the England midfielder as the best possible replacement for the likes of Andres Iniesta and Xavi, who are both approaching the latter stages of their Barcelona careers.
And the Catalans feel 21-year-old Wilshere has what it takes to be a mainstay of the Barcelona midfield for years to come.
Arsenal however, have no interest in selling one of their most prized assets.
Wilshere only recently signed a new five year deal at the Emirates, and has previously stated he hopes to stay at Arsenal for the duration of his career.
Arsene Wenger will also be aware the uproar it will cause amongst Arsenal fans should one of their homegrown talents be allowed to leave.
The club have been keen to stress the days of selling their best players is gone, so it is likely any bid from Barcelona will be flatly rejected.
It just remains to be seen whether Wilshere will be tempted by a move to the Spanish champions.
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