The letter from Janner, who last month was deemed unfit to stand trial for 22 child sex abuse charges, was penned on House of Lords paper with his signature clearly visible at the bottom.
It comes days after Scottish police launched a new probe into the former MP for allegedly sexually abusing a teenage boy.
Janner has always denied claims that he was a paedophile and his family say he is innocent of the alleged sex attacks.
The letter was given to Jackson's friend Mark Lester, who starred in the 1968 classic film Oliver! but never passed on to the pop star, according to Ben Griffiths at The Sun on Sunday.
|Best wishes: Lord Janner (pictured right) wrote a letter to Michael Jackson|
congratulating him after his acquittal on child sex charges.
The pair met during a tour of the Houses of Parliament
'I hope that you will return to London and that I should have the pleasure of seeing you once again ... so good luck and all best wishes. Yours, Greville.'
The pair first met when the peer showed the singer round Parliament in 2002.
Mr Lester found the note during a clear-out at his home in Cheltenham, Gloucestershire, and says Janner gave it to him during a charity do 10 years ago.
|Letter: Lord Janner gave|
the letter to Jackson's friend
Mark Lester (above) who said
it was 'inappropriate'
Director of Public Prosecutions Alison Saunders maintains that the peer is too unwell to be prosecuted in England, despite evidence that he may have abused children.
But 78 MPs have so far demanded Mrs Saunders change her decision with veteran Labour MP David Winnick saying Mrs Saunders should be called before the Commons home affairs committee.
The former MP for Leicester voted 203 times in the House of Lords even after he granted power of attorney to his children because of his dementia in 2009.
As Scotland has a separate prosecution system, authorities there could make a decision independently of the CPS review.