Rashford and Lindelof were forced off during the 2-1 Carabao Cup victory over Chelsea while Maguire was left hobbling at the end of the game at Stamford Bridge.
"It's still early," Solskjaer told a news conference on Friday. "Hopefully we can get them back on the pitch [at Bournemouth].
"They had some treatment on Thursday, a little more treatment today [Friday], a light session and hopefully they're ready. I can't exactly tell you exactly now."
Rashford has scored four goals in four games as United have recovered from a disappointing start to the season to win three away games in a row.
They face a Bournemouth side on Saturday who have not won since September and did not score at all in October as Solskjaer's men chase four away wins in 10 days.
"The confidence is getting better," Solskjaer said of his side. "Getting players back from injury helps.
"In football it's not very far from failure to success or other way round. Every game is a new opportunity to show what you can do and that's part of being here.
"I didn't play every game and every game I played was a chance to show the manager I should play the next one and hopefully these boys feel like that."
Before hitting his purple patch, Rashford had scored once in his previous nine games. His return to form has coincided with Anthony Martial's return from injury and Solskjaer has credited the France forward with helping to get the best out of his No.10.
"Since Anthony's come back Marcus has blossomed," the United boss said. "He's probably happier facing goal, being direct, driving at people, taking players on rather than [a] target man with [his] back to goal but Marcus wants to master all the skills."
Meanwhile, United are offering free travel to the Europa League fixture with FC Astana for supporters who had booked with defunct travel company Thomas Cook. The club have chartered a plane for around 150 fans to make the 6,000-mile round trip to Kazakhstan on Nov. 28.
A club spokesperson said: "We have been working through a range of contingency plans to minimise the impact of the Thomas Cook situation for our supporters.
"We are pleased to be able to confirm that Manchester United will be operating a complimentary trip to the forthcoming match against FC Astana in Kazakhstan for those who were impacted by the insolvency of Thomas Cook.
"Beyond the Astana fixture, we are investigating longer term options around facilitating European travel for our loyal fans."