But the Norwegian insists there is no rush to get business done, despite Borussia Dortmund placing a deadline of August 10 for a deal to be concluded.
United are locked in talks with the German club over the structure of Sancho’s proposed move to Old Trafford, which would see them pay £60-70million up front, followed by instalments worth around £45m.
Solskjaer is eager to avoid a repeat of last summer, when he had to wait until close to the end of the window to complete the signing of Harry Maguire and the departures of Romelu Lukaku and Alexis Sanchez.
But United refuse to be rushed over Sancho, who they have pursued for over a year.
Solskjaer said: “This transfer window is a long one and every transfer takes its course. I’ve got no updates at the moment.
“We are always looking to improve the team and squad.”
Solskjaer wants to bring in at least three signings after securing a return to the Champions League.
Jack Grealish is also a target, while the United boss could look to strengthen in the centre of defence.
But he has also offered hope to Chris Smalling after the defender’s loan deal at Roma came to an end.
“Chris has shown how valuable he is,” he said. “This season was about him being a regular. I wanted to give Harry, Victor (Lindelof) and Axel (Tuanzebe) a chance.
“I have been speaking to Chris throughout. I have been delighted with his season.”
Smalling is still expected to depart, while Phil Jones could also move on after another season in which he’s struggled with fitness and form. Marcos Rojo is also expected to leave.
Solskjaer is a long-term admirer of Kalidou Koulibaly, but Napoli’s valuation is likely to rule him out of a move, even if the Italians lower their expectations from the £90million they wanted last summer.
Solskjaer previously dismissed links with City-bound Nathan Ake and praised his defence ahead of Wednesday’s Europa League round of 16 second-leg tie against LASK.
“I think we have been very, very solid at the back,” he added. “I think sometimes you might be exposed in behind when you are pressing as high as we have done.
“We have decided we are going to be a high pressing side when we can and if you don’t take risks, you don’t improve.
"Once in a while we’ve been found with some space behind us, but I’m not concerned about us.”