Solskjaer hailed Edinson Cavani after Sunday's Premier League win over Spurs, saying United had missed having a traditional centre-forward of his calibre over the past few seasons.
But the Uruguayan star's future is uncertain, amid speculation the 32-year-old will return to South America once his current contract ends this summer.
United are also expected to target a top-class defensive partner for Harry Maguire this summer.
And they could find solutions at both end of their pitch if they follow Ferdinand's recommendation and sign Dominic Calvert-Lewin.
Rio Ferdinand says Man Utd should target Dominic Calvert-Lewin (Image: REUTERS)
The Red Devils legend has urged his former club to swoop for the 24-year-old this summer with the striker enjoying a fine season at Everton.
Calvert-Lewin is the top flight's joint fourth highest scorer with 14 goals, and has also netted another five in cup competitions.
Valued at £40million according to Transfermarkt, he would be a much cheaper alternative to either Haaland or Kane - either of whom would cost upwards of £100m.
And that would leave funds in United's transfer kitty for Solskjaer to bring in a new centre-half.
"Listen, Dominic Calvert-Lewin for me, I love him,"Ferdinand told hisFIVE YouTube channel.
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"I’ve watched a lot of Everton this year and he’s one that unnerves defenders. He’s not one you want to play against week in, week out. He’s aggressive, he attacks the ball."
Ferdinand believes Calvert-Lewin has improved his game under Carlo Ancelotti, with the Everton boss having passed on tips from when coached Filippo Inzaghi at Juventus and AC Milan.
The former United defender said: "I was speaking to Carlo Ancelotti earlier this year and he mentioned Inzaghi and said he didn’t need many chances to score goals, and he scores goals in and around the six-yard box.
"I look at Calvert-Lewin this season and he’s listened to that, he’s taken that on board. Obviously, he seems a real good student of the game and he’s started putting that into his own game.
Everton striker Dominic Calvert-Lewin has scored 14 Premier League goals this season (Image: GETTY)
"I think he’d be a fantastic signing for Manchester United," he added.
"It’s one out of left field a little bit but I think he’d have a big impact," said Ferdinand. "He’d get on the end of the things created by Fernandes, Pogba, Rashford, Greenwood, etc."