The Gunners failed with a bid for the Scotland international last week after falling short of the Hoops’ demands for a down payment.
However, the Daily Mail reports that Arsenal are now close to agreeing a deal after restructuring their £25 million proposal.
Tierney is said to want a move to the Premier League, and the Scottish champions will allow him to leave if they receive an adequate up-front fee.
Unai Emery is eager for a deal to be completed soon despite harbouring some concerns about the 22-year-old’s pelvic problems.
Napoli were also been linked with a move for the Scot, but coach Carlo Ancelotti has since ruled out the possibility after deciding to stick with Faouzi Ghoulam and Mario Rui.
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