Blackburn had attempted to sign Van Nistelrooy, 34, from Real Madrid in 2009 but then-manager Sam Allardyce was forced to admit defeat as the club could not match his wage demands.
However, Blackburn owners Venky's have been eager to make a marquee signing and, with Van Nistelrooy out of contract at the end of the season, he would represent an attractive option.
Kean, who was at Emirates Stadium to watch Scotland take on Brazil in Sunday's friendly, told ESPNsoccernet: "Yes, I can confirm we are interested."
Michel Salgado, who spent ten years with Madrid before joining Blackburn in 2009, has a good relationship with Van Nistelrooy and it is hoped that he will help lure the striker to Ewood Park.
Van Nistelrooy - who was denied the chance to return to the Bernabeu in January when Hamburg blocked the move - has said he would welcome the chance to return to England.
"I am thinking about a nice club in England after this season, or a club in Spain, but I don't think Real Madrid will come again after their efforts to bring me back in the January transfer window," Van Nistelrooy said in the Sunday Mirror.
"I have decided that if a really big European club does approach me, I will accept a role as reserve striker. I would have accepted that too if the deal with Real Madrid had come off in January.
"They knew I was ready to step in when needed."