The People says the 31-year-old Republic of Ireland international is keen to move on after a fall-out with Kean last summer.
He had a successful loan spell at IPSWICH until he suffered a torn hamstring.
Last month he was weighing up offers from Premier League trio Aston Villa, Wigan Athletic and Swansea City. Ipswich would love to keep him and Andrews knows he needs to play regularly if he is to keep his place in the Irish squad heading for Euro 2012.
But, although he still has 18 months of his Blackburn contract to run, Andrews does not want to play for Kean again. He would prefer to move elsewhere.
But because he is currently crocked, his hopes of a transfer are on hold and he could have no option but to stay put.