Boro are in desperate need of defensive reinforcements following Robert Huth's sale to Stoke.
With Emanuel Pogatetz still some way short of fitness, Matthew Bates out for the season and Chris Riggott also sidelined, Boro have very few experienced options in central defence.
David Wheater, who is set to skipper the side in Pogatetz' absence, is the only player with any real first-team experience available to Gareth Southgate.
He has already failed to loan Matthew Killgallon and Sean St Ledger from Sheffield United and Preston respectively, but looks set to succeed with his move for Khizanishvili.
The 27-year-old Georgian looks to be surplus to Sam Alladryce's requirements at Ewood Park, having featured just once for Rovers this season.
It is understood talks are ongoing over Khizanishvili and Boro are hopeful a deal will be completed before this weekend's clash with Ipswich.
Boro are also still trying to bring in a new striker, and with a deal for Rob Hulse remaining unlikely - they could yet rekindle their interest in Heidar Helguson.
The former Watford man had been set for a loan move back to Vicarage Road on deadline day, but that deal failed to materialise and he could be interest in a move to the Riverside Stadium.