The Mirror says Lambert has been promised all of the £37million windfall from television income to help strengthen the squad as the Canaries look to avoid a swift return to the Championship.
The 41-year-old Scot - who has presided over back-to-back promotions since arriving in August 2009 with Norwich near the foot of League One - is understood to be keen on improving the spine of the side and has been linked with Leeds duo Robert Snodgrass and Bradley Johnson.
Newcastle United goalkeeper Fraser Foster, who enjoyed a successful loan spell at Norwich in their League One campaign, and Manchester United's Belgian defender Ritchie De Laet are also reported targets.
Veteran striker Miroslav Klose is another said to be on Lambert's radar, the Norwich manager maintaining close ties in Germany from his time with Borussia Dortmund, where he won the 1997 Champions League.
The 32-year-old, who has scored 61 goals in 108 caps for Germany, is out of contract with Bayern Munich this summer, and could be tempted to the Premier League, but AC Milan and Valencia are also both watching developments.