All three players were embroiled in controversy last month when Maguire was handed a 21-month suspended jail sentence by a Greek court for aggravated assault, resisting arrest and attempted bribery following an incident while on his summer break in Mykonos.
Greenwood and Foden were sent home from the previous camp in disgrace after breaching team rules and coronavirus protocols by meeting two women in a different part of the team hotel in Iceland, outside of the squad's bubble just hours after making their senior debuts.
Solskjaer voiced his concerns over Greenwood's initial call-up and then the Football Association's decision to put the 19-year-old forward for media duties.
However, Southgate said: "I have spoken to Ole. I felt that was important because the best way for us to communicate is always directly so we had a really good chat at the end of last week. We're actually on a similar page on a lot of things: the idea of looking after young players is very important in how we develop them.
"The only thing where there was a misunderstanding, we did have contact from the club, they were still in Europe [into August] and wanted to know whether there would be dispensation for the clubs that were still in Europe [after the end of the last Premier League season]. That was understandable because it was a very difficult situation for Manchester City, Manchester United, Wolves, Chelsea.
"But because we had four clubs in that situation and what that would mean in the knock-on effects for other clubs, we just couldn't help that."
Southgate insisted that Maguire's return to the squad was a foregone conclusion while Foden and Greenwood needed time to reflect on their actions.
"I said last month there was absolutely no reason we couldn't pick Harry this time and he has been our most reliable defender over the last couple of years so it was not even a consideration in terms of whether he would be in the squad or not," said Southgate.
"With what happened [regarding Foden and Greenwood], there are two parts. We have to send a message to all our players in our teams at every age level that sort of thing isn't how we do things with England.
"But then we have also got to rehabilitate these two boys. These lads have suffered now enough. We didn't think it was right, they need this period of reflection but then that gives them the opportunity to get back on their feet with their clubs.
"They are both starting to play well again, which is important, and then I can speak to them after this camp and it will be about their form then as to whether they are selected next time around."
Southgate, who selected three players for the first time in Arsenal's Bukayo Saka, Everton's Dominic Calvert-Lewin and Leicester's Harvey Barnes, aimed a mild-mannered dig at Jose Mourinho after the Tottenham head coach insisted his players could not play in three international matches following a hectic start to the domestic campaign.
Referencing Mourinho's comments about his friendship with Steve Holland -- now England assistant manager but formerly on Mourinho's staff at Chelsea -- Southgate said: "Jose was great wasn't he? He's on good form. I heard him.
"He won't phone but he's going to stand at the top of Tottenham's stadium and tell us so that was good. I was a bit disappointed I'm not one of his friends, I know Steve is.
"In fairness, Steve helped him to a league title so that's understandable. We certainly are not looking to start players in three games. I can't guarantee that no player will play no minute of all three games.
"You might end up having to put someone on for five minutes and then people will be saying 'you didn't do what you said.' But our aim is to manage the squad. We have got to be responsible. We are conscious of the welfare of the players. The season as a whole is a huge challenge for clubs and national teams. So we've all got to work together.
"It doesn't help anybody if we aren't joined up on our thinking and all Jose needs to do is make sure in April and May that he has got to look after Harry Kane for us because there will be 55 million people relying on that. That obviously works both ways."