Boro are looking to strengthen after losing Robert Huth to Stoke City and other defenders being injured.
Gareth Southgate has tried to bring in Matthew Killgallon and Sean St Ledger on loan deals but that has failed so now a move for Khizanishvili looks to be on the cards.
The 27-year-old Georgian international looks to be surplus to Sam Alladryce's requirements at Ewood Park and it is understood talks are ongoing over Khizanishvili and Boro are hopeful a deal will be completed before this weekend's clash with Ipswich Town.