Villa close to Allback deal - claim
The 28-year-old has been strongly linked with a move to Britain, with Sunderland, Southampton and Rangers known to be heading a queue of clubs.
However, King has now been quoted as saying that Villa are set to land the former Bari man.
"Our manager Graham Taylor likes Scandinavian players for their attitude," King told Svenska Dagbladet.
"We are very close to signing him, he is our kind of player. Smart, and knows what he wants."
Allback has been in prime form this season with 14 goals in 28 games and Villa were known to have watched him score last weekend in the 2-1 win over De Graafschap - where they were also watching goalkeeper Stefan Postma.
The Swede has always stated that he will be leaving The Abe Lenstra in the summer, when a clause in his contract allows him to depart for just £2 million.
