The same paper reported last month that Lavery (below, centre) had turned down the Owls' offer of a new contract, though other reports claimed talks were still ongoing.
However, with no updates arriving in the meantime, it would appear the 23-year-old's future lies away from Hillsborough and a cross-city switch could be on the cards.
According to the Star, Lavery was at Bramall Lane to watch the Blades' 1-1 draw against Rochdale on Saturday - an act that was interpreted by the club's hierarchy as a signal he wants the move.
However, United officials reportedly insisted that no talks were held with the player ahead of the game.
United, who've already added one ex-Wednesday striker in Leon Clarke (above) this summer, sold Che Adams to Birmingham City earlier this month and are thought to be seeking a replacement.
Despite his contract status the Blades would have to pay compensation for Lavery, due to his age and the fact he was offered a new deal at Hillsborough.
The Northern Irishman arrived in the Steel City from Ipswich Town four years ago and played 39 times for the Owls, scoring on six occasions.
However, he found opportunities hard to come by under Carlos Carvalhal and spent time on loan to Portsmouth last season, where he partnered current Blades striker Marc McNulty (above).