The Catalan giants - amid devastating financial turmoil - were mostly restricted to the signings of free agents in the most recent window as Eric Garcia, Sergio Aguero and Memphis Depay all joined the club.
However, with president Joan Laporta setting his sights on big-money moves for next year, Mundo Deportivo claims that a triple swoop for Pogba, Olmo and Haaland is the "dream" for the Barcelona chief.
Pogba is yet to agree to an extension on his Manchester United contract beyond the summer of 2022, and the Blaugrana are reportedly hopeful of agreeing a free transfer for the France international next year.
Meanwhile, Olmo is understood to be wanted by Barca, Man United and Real Madrid, but the playmaker recently poured cold water over speculation that he could complete a move away from RB Leipzig.
With regards to Haaland, Barca are one of many clubs expected to battle for the Norwegian's signature when his £68m release clause activates next summer, but the club's economic vice-president Eduard Romeu is fearful that Real Madrid may be in pole position for the striker.