The Hoops are understood to have made contact with the U’s over the possibility of signing Eastwood on transfer deadline day as an emergency replacement for the injured Craig Gordon.
Eastwood, 28, has had spells at Huddersfield, Woking, Bradford City, Halifax, Portsmouth and Blackburn Rovers as well as Oxford.
With Gordon sidelined for 12 weeks and third-choice goalie Conor Hazard on loan at Falkirk, Celtic boss Brendan Rodgers has back-up goalkeeper Dorus De Vries and development team ‘keeper Ross Doohan as his only options between the sticks.
With Europa League matches against Zenit St Petersburg coming up, Rodgers was keen to acquire experienced reinforcements, and made an approach for Motherwell ‘keeper Trevor Carson before Bain joined on loan from Dundee.
Celtic were also linked with Kieren Westwood as Rodgers cast his net wide in a bid to bring in the right man.
Celtic’s interest in Bain sparked something of a loan deal merry-go-round, with the goalie’s loan deal at Hibs being cancelled, while Hibs striker Simon Murray was loaned to Dundee and Celtic loaned Scott Allan to Hibs after the midfielder’s loan agreement with the Dens Park side was ripped up.
While no move for Eastwood materialised, Celtic could reignite their interest during the summer - although they could face competition from Barnsley for Eastwood.
The Tykes were linked with a move for the former England Under-19 cap during the window.