The Red Devils were linked with a move for the 28-year-old winger earlier in the summer transfer window, but there is yet to be any confirmation of an official deal for the Croatian.
Manchester United were thought to have put their bid to try and sign Perisic on hold in recent days, but journalist Sheth claims that the Red Devils have now re-opened talks with Inter Milan.
He also claims that the Italian club are likely to want a fee in the region of £44m for the winger.
Speaking on Sky Sports News HQ on Tuesday morning, Sheth said: “Talks have resumed with Inter Milan and Manchester United are prepared to increase their opening offer.
“Inter’s asking price is believed to be around £44m.”
Manchester United have been linked with a host of players this summer, but the Red Devils have so far only concluded a deal to sign defender Victor Lindelof from Benfica.
The Red Devils are gearing up for a return to the Champions League next season after Jose Mourinho led them to Europa League glory in his first campaign in charge last season.
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