Despite turning down a £2m offer from the Gunners and slapping a £4m tag on the 37-year-old, Fulham accept Schwarzer will be going to the Emirates.
So they are lining up a move for former Scotland keeper McGregor, 28, rated at £2m by Rangers although the Cottagers aim to do business at about half that.
McGregor and Scotland captain Barry Ferguson were dumped from their national team after a late night drinking session.
The pair landed themselves in further trouble days later when they made obscene gestures at cameramen while on the bench.
And five months ago, McGregor, also on West Ham's radar, was the victim of an alleged attack by Celtic supporters outside a Glasgow nightclub.