The Canaries have spent less than £4m on new faces this summer following their promotion back to the Premier League, while fellow newcomers Aston Villa and Sheffield United have splashed over £133m and £42m respectively.
According to French publication Le Telegramme, the side are set for a late splurge and have had a €16.5m (£15.2m) offer for Claude Maurice accepted by Lorient.
The outlet claims that the player - also linked with West Ham United this summer - will now make the decision on whether to switch Ligue 2 for the Premier League before tonight's 5pm transfer deadline.
Should Claude Maurice opt for a move to Carrow Road, he will become the club's most expensive ever signing, almost double the £8.5m paid to sign Timm Klose in January 2016.
The France Under-20s international scored 14 goals in 35 Ligue 2 appearances for Lorient last term.