Australian Mott made an ideal start in his new role with a 3-0 one-day clean sweep of the Netherlands, a result that was largely expected even if England's record-breaking batters broke new ground in Amstelveen.
Attention now turns to more competitive series against India and South Africa, with 12 limited-overs matches - three ODIs and three Twenty20s against each nation - between between July 7-31.
While Mott would relish having his best available side to prepare for this autumn's T20 World Cup, he is mindful of red-ball head coach McCullum's needs.
All-format players Ben Stokes, Jonny Bairstow and Joe Root will almost certainly be required for England's Test assignments against India and the Proteas.
Following the end of England's third Test against New Zealand at Headingley, Mott plans to catch up with McCullum for the first time since they took up their posts to discuss their respective positions.
For now, though, managing director of men's cricket Key will ultimately be responsible for charting a path for the summer and where the players will be needed most.
"We've all come in at pretty much the same time so we're all open to getting the best way to work through things and getting face-to-face next week will be really important for that," said Mott.
He stressed his early days in charge have included a lot of "listening and learning" but it's clear he has the utmost respect for what Morgan has achieved during his time as captain.
The 2019 World Cup-winning skipper made two successive ducks against the Netherlands and has just one half-century in his last 65 innings in all matches.
He then missed the final ODI as a precaution because of a tight groin, an injury which first surfaced when he was on Middlesex duty last month.
Form and fitness issues have led to speculation about how long Morgan will remain in the job but Mott has full faith in the 35-year-old, who has outlined his determination to lead England at the T20 World Cup.
"He'd love more runs, most batters do," the Australian said.
"He's been a class player and over 200 games he's been a very, very good player and I don't think that's going to change.
"Of course he'd love to get some runs and there's some opportunities coming up. Having sat out this game, I'm sure that will light the fire a little bit for him for the huge summer ahead."
England may be 50-over world champions and ranked second in both white-ball formats but Mott, who oversaw sustained success for Australia Women, is optimistic they can develop further.
"What you want to do is keep pushing boundaries and keep trying to get better," he added.
"It's very early to be making too many big statements but I definitely think this team is capable of more."
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