The West Ham United midfielder has been out of action for the past two months.
The 27-year-old joined the Hammers on a free transfer from Arsenal in the summer of 2018, but injuries have hampered his progress at the London Stadium.
Wilshere has made just five Premier League appearances for West Ham, and has not played since injuring his ankle in December.
The Englishman is on a lucrative salary in east London, so Pellegrini will be desperate for him to come back as soon as possible, and to start earning his money.
The Chilean spoke to reporters today, and responded when asked when he expects to have Wilshere back and available for selection, as quoted by Football.London:
"Jack [Wilshere] will finish his eight weeks after his ankle surgery next week. He will return to different work and then we will see how he is."
West Ham currently have so many first-team stars out injured, and when they return to action, Pellegrini's men will surely be looking to kick on and make a sustained push for the top seven.
Whether Wilshere will be in a fit state to contribute between now and the end of the season, however, remains to be seen.
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