The Canaries are set to return to the Premier League for the first time since 2005 after securing back-to-back promotions under Lambert, who took charge in August 2009 with the Norfolk club near the foot of League One.
The 41-year-old former Celtic and Motherwell player is set to put pen-to-paper this week according to Norwich's deputy chairman Michael Foulger.
Lambert, who won a European Cup winners' medal with Borusia Dortmund, has attracted the interested of a number of English clubs including West Ham and Burnley.
He has been involved in lengthy discussions with the board over improvements to his rolling 12-month deal.
Norwich deputy chairman Michael Foulger revealed those negotiations are now close to a satisfactory competition.
Foulger told BBC Radio Norfolk: "Can I just say there'll be some great news regarding the manager situation that we will hope to announce this week.
"This success to me rates as the very best in my time as a board director.
"We don't have any superstars, but what we did have was a fantastic group with a tremendous team spirit and those lads would run through a brick wall for the manager."
Lambert has been promised all of the 37million windfall from television income to help strengthen the squad to avoid a swift return to the npower Championship.