Solskjaer wants more new arrivals, with central defence and midfield identified as areas in need of improvement.
"We are quite calm,” Solskjaer told MUTV, when asked to reflect on United’s summer business to date. “We have been good in the market so far and we’re still working on a case or two.
“I have been in touch with Joel [Glazer, chairman], Ed [Woodward, executive vice-chairman] and the recruitment department over the summer.
“There will probably be some more business done but happy with what we have done so far.”
Solskjaer is leading a summer rebuild at Old Trafford after the disappointment of finishing sixth last year and failing to qualify for the Champions League.
And as well as the signings of Wan-Bissaka and James, United have tied down Marcus Rashford, Juan Mata, Andreas Pereira and Axel Tuanzebe to new contracts.
“I’ve got to say it’s been very good so far,” Solskjaer said. “I’ve got the backing and we’ve got the people we wanted, for now. There will probably be some more business being done.”
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