Bit on Tuncay, bit on Johnson and Downing:
Southgate confirmed on Thursday the 24-year-old England international - who has been linked with Aston Villa, Tottenham and Everton among others this summer - has been told he can step up his recovery after foot surgery.
However, he will miss the start of the season and is unlikely to play until much later this year.
Downing has a gentlemen's agreement with chairman Steve Gibson that he can leave his home-town club for the right price - thought to be in the region of £12million - after he rejected Spurs' latest bid in January.
His injury, suffered in a challenge with Aston Villa's Stiliyan Petrov in May, looked to have scuppered hopes of a big money move - although Southgate today admitted he does not know what the future holds for the star graduate of the club's Academy.
He said: "He won't be fit for the start of the season, but it depends whether clubs want to take him now.
"Come January, there might be four or five other clubs involved.
"That's for other clubs to decide. We will just focus on getting him fit as quickly as we can.
"He went to see the surgeon, who did the operation on Tuesday - and he was very pleased with the progress.
"He is where he hoped he would be, perhaps a little bit further ahead.
"We still think it will be the later part of the year, but he is progressing very well."
Southgate knows he is unlikely to be able to hold on to the likes of Downing and Turkey international Tuncay Sanli, with Villa reportedly lining up a £20million joint bid for the pair.
In addition, speculation has suggested England Under-21s winger Adam John is an £8million target for Chelsea.
However, the Boro boss insists - while the Teessiders have valuations for those players who may be in demand - they have as yet received no formal offers for any of them.
He said: "We have internally in terms of what you would take - you have a valuation for every player in your squad at any time.
"But it's not for us to make those public. If other clubs have an interest, then they have to make contact with us and make us an offer.
"I have had telephone conversations with various people, but at the moment we haven't got any bids on the table."
That said, he does not expect to be able to keep Tuncay, who is currently enjoying an extended break after representing his country since the end of last season.
Southgate said: "I would expect that for a player of his quality - and not only his quality, but his character as well - there would be a lot of interest in him.
"The market has been fairly quiet, generally speaking, up to now. But I wouldn't think we would be able to hang on to a player of his talent and his ability.
"He is an international player. We have got quite a few players I would class as Premier League players, but he is certainly a top-half Premier League player."
Southgate confirmed that, while Afonso Alves is now on Teesside after missing the first two days of pre-season training, Mido is not - and that both men will be punished.
He said: "Afonso is back in training; Mido isn't back yet. We know when we are expecting him back.
"He should have been back on Monday. He was not - we have dealt with it. Both the players will be disciplined - end of story, as far as we are concerned."