Experienced Uruguayan international Cavani initially moved to Old Trafford on transfer deadline day in October, three months after a trophy-laden seven-year stint at Paris Saint-Germain ended with his release.
The former Napoli and Palermo frontman - who turned 34 earlier this week - penned an initial one-year contract at United, with that deal now having just four months left to run.
However, Cavani’s deal contains the option for the Red Devils to extend by a further 12 months and Solskjaer says discussions are due to take place shortly with a player who has made a key impact in a short space of time, scoring seven goals in 24 appearances across all competitions.
“I can only say Edinson has done well,” the Norwegian told reporters at a press conference held before Sunday’s visit of Newcastle in the Premier League.
“He’s really gelled in the group and we’ll sit down and speak with him in the near future to see his plans and ours. It’s a good discussion to have.
“We always speak to the players and, with the contract situation at the moment, we’re very pleased with what he’s done.”
Cavani missed Thursday’s 4-0 Europa League last-32 first-leg win over Real Sociedad in Turin with an undisclosed muscle injury, though Solskjaer is hopeful that both he and fellow summer signing Donny van de Beek will be fit to face Newcastle.
“They’ve got a chance, I think, so we’ve just got to give them until before training on Saturday as we need to pick a team on Saturday,” he said. “We’ll see how they are and hopefully they can both be available.”
However, Paul Pogba is not expected to return from a thigh injury suffered in the recent 3-3 draw with Everton until next month.