talkSPORT also understands that the Gunners and Moncao are still trying to reach an agreement for the sale of Folarin Balogun.
Tierney joined Arsenal from Celtic in the summer of 2019 but struggled for game time last term with just six starts in the Premier League.
And the Scotland international looks set for time away from the club with the surprise move to Spain now on the cards.
Balogun returned to his parent club following a successful loan spell at French side Reims.
The forward has been heavily linked with a move away from the Gunners with Chelsea among the clubs reported to be in contention.
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However, Monaco is his most likely destination and talkSPORT understands negotiations are still ongoing between the two clubs.
Monaco had a formal offer for the 22-year-old rejected earlier this month but the Ligue 1 side's sporting director, Thiago Scuro, is said to have a strong relationship with his opposite number at Arsenal, Edu.
Balogun enjoyed a successful loan spell with Will Still's Reims, finishing fourth in the French top flight's goalscoring charts with 21 goals in 37 appearances.
He has represented England at under-17, U18, U19 and U21 level but the Brooklyn-born player committed his international future to the USA earlier this summer.