The Canaries secured an instant return to the Barclays Premier League when Alex Neil's side beat Middlesbrough 2-0 to win the Sky Bet Championship play-off final at Wembley, and with it the prospect of over £130million in new income.
Scotland midfielder Graham Dorrans has already seen his loan move made permanent, and McNally expects more additions to follow, but not in great numbers, with Youssouf Mulumbu, released by West Brom, one reported potential target.
"The squad is strong, but we need to support the strong players in a way that ensures anyone who joins improves the group
We are going to be very careful that happens," McNally said in an interview with the Eastern Daily Press
"We will see what the summer brings, but I think we would be happier if it was five, six or seven players joining than 10, 11, 12 to give us more chance to ensure they can fit in."
McNally added: "We have greater knowledge in the domestic market than we have the international markets, but if we were bringing in six or seven the chance is the majority will be British-based players, although in the Premier League you also have to be aware of the international scene and look to Europe for one or two."
Norwich have yet to decide on the future of record signing Ricky van Wolfswinkel, who spent last season on loan at French club St Etienne, scoring half-a-dozen times in Ligue 1
The 26-year-old Dutch forward joined the Canaries from Sporting Lisbon for £8.5million in July 2013, but managed only one goal before suffering an injury setback and had a limited impact as Chris Hughton's side fought an unsuccessful battle against relegation
Source : PA
Source: PA