They claim Spurs have accepted the offer, although the London club is still refusing to comment.
Keegan wants a left-sided defender, and Reading full-back Nicky Shorey is a more obvious target for Newcastle United.
The England international is certain to leave the Royals this summer following their relegation from the Premier League, and he has already been linked with a number of clubs.
Toon Set To Sign Spurs Defender?
Portsmouth emerged favourites for his signature, but Kevin Keegan, desperate to bolster his back four and who has stressed his desire to sign a left-back, has entered the race and is willing to pay Reading's asking price of £3.5million.
Shorey has just one year remaining on his existing deal at the Madejski Stadium, and he will be hoping a move to a bigger club will increase his chances of forcing his way into Fabio Capello's plans.
Watch this space.