The City board did say there would be no more transfer dealings after spending a massive £23 million on new players this summer and Keegan has still to decide whether to offer a permanent contract to Kerkar, who was recommended to him by new City captain Ali Benarbia.
Bernstein said: "Everything, of course, hinges on whether our manager believes that Kerkar would be a useful addition to his senior squad.
"But there is certainly some flexibility remaining in our transfer activities and we have not ruled out the possibilty of adding another player to the wage bill if Kevin believes it is in the club's best interest.
"We will not be taking on any more major financial commitments prior to the start of the season but there would be no transfer involved in signing Kerkar on a permanent basis so bringing him to the club on a permanent basis shouldn't be a major problem.
"I am sure that Kevin will agree that we have done everything we said we would do towards improving the senior squad in readiness for the coming Premiership campaign.
"In terms of numbers and quality we feel we are just about there but of course there is an exception to every rule and if Kevin feels that Kerkar is an exceptionally talented player who will bring something extra to his squad then he will find us very supportive about a permanent contract for the player."