The Belgian defender looks set to leave the Emirates Stadium in the summer after falling down the pecking order under Arsene Wenger.
He is understood to be ready to quit the club in the coming months in search of regular action, which has alerted Mourinho.
‘The Special One’ is keen to further bolster his backline in the off-season, with John Terry’s long and illustrious career coming to an end.
Although Arsenal might have reservations about doing business with a direct and local rival, Vermaelen’s contract will enter its final year soon which could leave him available for a free transfer in 2015.
Manchester United have also been linked with the 28-year-old, but the lure of Champions League football at Stamford Bridge may be a deciding factor.
Mourinho is also attracted to Vermaelen’s ability to fill in at left-back, which could be a bonus with Ashley Cole set to leave west London in the coming months.
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