Sky Bet suspend betting on Radamel Falcao's next club after seeing him backed at as short as 1/3 to join Real Madrid.
Morgan Schneiderlin has appealed to Southampton fans after a thwarted attempt to leave St Mary's.
Stock's move to Turf Moor from Doncaster on a two-year deal reunites the 30-year-old with former Bournemouth team-mate Howe.
Stock is Howe's sixth summer signing and the Clarets chief told the club's official website: "Brian is a very good footballer who will suit how we play.
"He is someone we admired for a long time. He had a really good career at Doncaster and I thought he was impressive in the games he played against us over the past couple of years.
"Experience and leadership are two things we haven't got a great deal of and I certainly think he will add in those two areas."