Boro, for whom Huth also played, were initially installed as 6/1 shots - behind Cardiff City (4/1) and alongside Aston Villa and Stoke City, another of the German's former employers.
But the Teesside club have seen been cut to 4/6 - ahead of Stoke (3/1).
Leicester confirmed Huth's release last month, after the 33-year-old suffered an injury-ridden campaign.
And with Middlesbrough's Ben Gibson strongly liked with a move to the Premier League, it is possible the beaten play-off semi-finalists could turn to Huth as a replacement.
The ex-Chelsea stopper spent three seasons at the Riverside Stadium, but left for a Stoke side then managed by Boro boss Tony Pulis, in 2009.
Aston Villa, Derby County and West Bromwich Albion are all 12/1 to land Huth.
Leicester moved fast to replace the 19-cap former international, landing West Brom's Jonny Evans for a cut-price £3.5 million.