The 34-year-old Uruguay international has impressed on and off the pitch since joining on a free transfer from Paris Saint-Germain in October.
Cavani, PSG's all-time top-scorer, signed a one-season deal with United with the option to extend by a further year.
He has scored seven goals in 24 appearances for United and Solskjaer has made no secret of his hopes to keep him at Old Trafford.
"I've been impressed by him," said the United boss. "He's really gelled in the group and we'll sit down with him and speak with him of course in the near future to see his plans and our plans.
"It's a good discussion to (have). We always speak to the players and with his contract situation at the moment we're very pleased with what he's done."