It has been a season of struggle for Welsh outfit, with former manager Malky Mackay sacked in December and Solskjaer's appointment as the Scot's successor has not yet produced a reversal of fortunes.
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"If we get the results and performances over the next seven games and other clubs start looking at my players I will probably be happy," he told Wales Online.
"What it means that we will be in the Premier League next season."
Goalkeeper Marshall has been in particularly impressive form of late and recently agreed a new contract amidst rumours of interest from Tottenham - but the manager refused to comment on the speculation.
"David has just signed a new contract six weeks ago," Solskjaer added.
"He has been terrific this season and he is a vital part of my squad. He's going to be immense and phenomenal over the next seven games, I'm sure of that. He's been absolutely top.
"I've said he's in the top three or four goalkeepers in the Premier League."