When asked about Pogba's future during a press conference here ahead of United's friendly against Perth Glory, Solskjaer pointed out: "As far as I am aware and up till now, we do not have any bids for any of our players."
"He (Pogba) is a top, top bloke. He is a great professional. He is never been any problems. He is got a heart of gold," he added.
The 46-year-old boss said that he was confident goalkeeper David de Gea would pen a contract extension with the English club in the coming weeks.
"David has had a summer where he has been negotiating and thinking about his contract. We hope we are going to get it sorted soon," he stressed.
"I have said it many times how lucky I am and how happy we are to have him in the goal, so we hope he stays here for many years," Solskjaer added, referring to De Gea, who joined the English side from Atletico Madrid in 2011.
Solskjaer was also hopeful Chile forward Alexis Sanchez would regain his form soon.
"I do not think Alexis' injury was too bad. He is due back just three weeks after his last game so just after we come back from (the pre-season) tour here," he pointed out.
Sanchez picked up a hamstring injury during Chile's 2-1 loss to Argentina at Copa America on Saturday.
United is set to face Perth Glory on July 13, Leeds United on July 17 in Australia and Inter Milan in Singapore on July 20, before finishing their tour against Tottenham Hotspur in China on July 25 and AC Milan in Wales on August 3.
( With inputs from IANS )