The Norwegian was quizzed about the future of the 34-year-old after United were beaten 3-1 by Manchester City in the Carabao Cup semi-final first leg on Tuesday night.
Young was left out of the squad fuelling rumours that a move to Inter could happen.
However Solskjaer claimed not to know anything about reports linking the veteran with a move to the San Siro.
He said: "It's not the night to talk about players leaving. I don't know what you are talking about."
Solskjaer then claimed United need to bring players in, not let them go, but that does not mean a switch to the Nerazzurri will not happen sooner rather than later.
Young is out of contract at the end of the season and as things stand there is no sign of him penning a new one.
It is unclear at this stage whether Inter are working to get the player on board immediately or whether they want him to sign a pre-contract agreement with a view to making the switch at the end of the season.
Inter boss Antonio Conte is a big fan of the player and tried to sign him while he was in charge of Chelsea, but United refused to do a deal and he stayed at Old Trafford.
United then took up the option to keep hold of him for another season but he has struggled for action and is now looking to move on.
Inter are looking to make a number of new signings and Young could be one of many this month.