The Gunners have already splashed out £52million on Alexandre Lacazette but Arsene Wenger is keen to continue his summer spending.
And it seems Lemar is firmly in his sights as he looks to bolster his midfield with the signing of the talented 21-year-old.
Arsenal have been in negotiations with the Ligue 1 champions for some time but agreeing on a fee has proved difficult.
But Italian journalist Emanuele Giulianelli claims there has been a breakthrough and a deal has now been finalised.
Arsenal have reportedly agreed to pay £48m for Thomas Lemar Arsenal predicted starting XI with Thomas Lemar Fri, July 7, 2017
How could Arsenal line up if they signed Monaco starlet Thomas Lemar?
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How might the Arsenal starting XI look with Thomas Lemar?
Giulianelli states the Gunners have agreed to pay £48m, plus bonuses, to make him their third summer signing.
Arsenal are currently away on their pre-season tour of Australia and China and will not announce his arrival until they return.
Monaco have reportedly asked the north London outfit to delay the announcement until they find a suitable replacement.
Thomas Lemar is keen to work under Arsene Wenger at Arsenal
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Lemar is keen to get a deal over the line and move to the Emirates as soon as possible to play under Wenger and reports had suggested he was becoming frustrated at Monaco blocking his exit.
The France international is a big fan of Wenger and the chance to work with the 67-year-old is thought to be the main factor behind his decision to join.
Lemar, who is under contract with Monaco until 2020, scored nine goals and provided 10 assists last term.