The English Premier League side lost out to Borussia Dortmund on roping in highly rated
Erling Haaland.
But the manager said it is about getting the right players and he has the backing of the management.
"I'm always an optimist," Solskjaer was quoted as saying by ESPNFC.
"I'm optimistic we can keep players fit and if the right ones become available we do have the resources and I do have the backing from the board, but it's also about getting the right ones. It has to be.
"There's no point suddenly bringing someone else in now for the sake of three or four months if that can disrupt any good feeling or chemistry in the group, because the chemistry in the group is really good.
"It has to be the right type and it has to be a good investment for the long term as well."
United take on Arsenal on Wednesday after beating Newcastle and Burnley over Christmas.
"If we can keep on improving, one addition and if you get two additions of course that will be competition for places," Solskjaer said.
"That's what you've got to deal with at this club. We haven't had enough because we've had so many injuries.
"We're improving. I think we can see more and more of what we want to be and our identity and what we're good at. We're making games suit our style more and more. We're quite a bit away still from where we want to be but I think we're the youngest team in the Premier League on average," Solskjaer added.
( With inputs from IANS )