Sanchez has struggled to convince since arriving from Premier League rivals Arsenal in January past year, while former boss Jose Mourinho repeatedly called on United's hierarchy to spend more in the quest for success.
United are fifth in the Premier League, two points behind fourth-placed Chelsea, amid an undefeated start to life under Solskjaer since Mourinho's sacking in December.
Asked how many additions United would need in the summer to become title challengers, Solskjaer said: "It is about who we've got here as well".
Solskjaer believes the key to United regaining top spot domestically and in Europe will lie in maximising their existing talents.
Jones, 26, was due to become a free agent at the end of the season but the England global is now tied to United until at least June 2023, while the club have the option of a further one-year extension. "You get a different view on players but we're not too far away from when I came", he said.
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Ander Herrera could be the next player to extend his stay at Old Trafford as he negotiates a new contract with Manchester United, according to the Daily Mail. "We know at that moment there are some fantastic wingers in modern football: [Ousmane] Dembele, we have also [Raheem] Sterling who is a fantastic player, Anthony Martial, Eden Hazard... but I think Marcus is different".
Solskjaer laughed off the suggestion ahead of the trip to Fulham on Saturday, but the 45-year-old insisted that United should be aiming to challenge for the Premier League and the Champions League as early as next season. "They're the other games".
Speaking to Sky Sports, he said: "We all know what quality Paul possesses - Paul is Paul".
Pochettino had seemed to be the obvious choice to take the job permanently when Solskjaer took charge at Old Trafford, Rooney himself backing him for the role. "We're delighted Phil has committed his future to the club".