Except Basil understood Christ as the "Great God," there is no reason to entertain what follows: "did he think of Him as greater than the Father?" Besides that, Basil applies the whole verse to Christ.
From my reading, his quote does not call Christ the "Great God". In fact, you could see the quote in the opposite mode.
Basil, On John 17.3 (4th century), "Did the Apostle, when he styled the Saviour 'God over all,' describe Him as greater than the Father? The idea is absurd . . . When the apostle said of the Son, we look for 'that blessed hope, and the glorious appearing of the great God and our Saviour Jesus Christ,' did he think of Him as greater than the Father?"
It would be helpful here to add some commentary from Bible scholars, (perhaps Ezra Abbot and Hugh Stewart Boyd)
Also check for any additional references (checked, so far none except the one below.)
Here is a second spot where Basil uses the Titus verse, from ACCS: