They report the Newcastle star is set to join Manchester City for £4.5m and could have a medical today, according to reports.
The England international is on his way out of St James' Park because of unspecified "family problems" and Eastlands chief Sven Goran Eriksson is tipped to beat West Ham to the 28-year-old.
Yesterday Hammers chief Alan Curbishley admitted his interest and although Tottenham have kept very quiet on the subject, they have been watching the situation.
However, The Sun claims Eastfields is his prefered destination.
Dyer Has Played His Last Game For Newcastle!
He missed the 4-1 win over Celtic last night and Big Sam said it was "a precaution".
Sam Allardyce: "We were protecting our asset, there's a big value in him.
He could have played and been one of the casualties like Nicky Butt or Steven Taylor.
"It depends how long Nicky's injury is and who we buy as to if Kieron becomes more valuable to us. There's not been a bid in for him yet."