Japan international Shinja Kagawa, acquired from Borussia Dortmund, and former Crewe midfielder Nick Powell were presented to the media on Thursday at Old Trafford.
However, the 70-year-old admitted that he was still working on bringing further new faces into his squad.
He told the assembled reporters: "It's possible we could bring one more signing in, maybe two more. But probably one."
"We've always done well in terms of getting players at the end of the season, instead of waiting all summer," the Scot continued of those brought in already. "In Kagawa's case, there was a fair bit of negotiating and that kept going for weeks. As for Powell, we knew Dario Gradi [Crewe's director of football] would help us do the deal quickly."
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Whilst unveiling his latest recruits, the Red Devils boss hinted that the signing of Kagawa in particular could help bring back the title to Old Trafford, having lost out to local rivals Manchester City in 2011-12.
"Kagawa will play further forward," he divulged. "We shouldn't be looking at one player changing the way we play but he could make a difference.
"He can give us that extra in the final third of the field. If his goalscoring record continues he could be a very good player for us.
"Once he's adapted and gets to know some football phrases our players will use, he'll be used to that. He can start the first league game quite easily. I've got no problem with that."
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"I think in Nick's case, he's got a bit of physical development to do, just as we would expect of an 18-year-old. But he'll be in the first-team squad and train with us every day," the veteran boss continued.
"Football throws up opportunities for young players and we play young players all the time."