City have been one of the busier Yorkshire sides in the first half of the summer, bringing in four players so far in midfielders George Moncur and Andy Cannon, winger Randell Williams and keeper Nathan Baxter, the club's latest addition who joined on a season-long loan from Chelsea at the end of last week.
McCann, whose side start the new Championship campaign with a trip to Preston on August 7, is keen to bring in several other new recruits.
Priorities include bringing in a new central defensive option and another centre forward, while beinging in another midfielder is another target area for City, who have been linked with several players including former loanee Regan Slater and Middlesbrough's Lewis Wing, who spent the second half of last season on loan at Rotherham United.
McCann said: “Yes, it was very important that we did some of our business early, just like last year when some came early and some came a wee bit later.
“It was important to get them in (four new signings), they met the boys on Friday when they came in to get Covid tested.
“It’s nice to have the four in, we’re hopefully going to add some more additions maybe next week or the week after.
“We’re working very hard on that still.”
City began pre-season preparations at their Cottingham training base on Monday.