Cavani joined United as a free agent on a one-year deal at the start of the season and the 34-year-old has impressed in Manchester, where the Uruguayan has scored seven goals and supplied two assists across 25 appearances in all competitions.
Paris Saint-Germain's all-time leading scorer, Cavani has been linked with Argentinean powerhouse Boca Juniors after comments made by his father Luis.
But Solskjaer said United, which is second on the Premier League standings, is in talks with Cavani over his future at the Red Devils.
"We're speaking to Eddy," Solskjaer said ahead of Monday's (AEDT) FA Cup quarter-final against Leicester City.
"Edinson is a top striker and whatever he decides to do, let's see. We're in good dialogue with him.
"We want a competitive squad and we need someone up there to score the goals for us. So we're looking at it."
Earlier this month, Cavani's father Luis claimed the veteran was not happy in the Premier League and "would like to play for Boca".
"My son is not happy in England and wants to return nearer his family. He wants to play in South America," he said.
"I want Edinson to play for a team which fights for important trophies. He has had many conversations with [Boca vice-president Juan Roman] Riquelme and would like to play for Boca.
"At the halfway point of the year, he'd like to return to South America. My son’s idea is not to continue there [in Manchester]. He wants to return.
"I think he's going to come back in June this year."
Cavani Sr cited his son's punishment by the Football Association (FA) for using a racially insensitive word in a social media post as a factor in his unhappiness.
"There are things which sometimes annoy us as humans, as people. The whole ban issue annoyed him," Luis Cavani added.
"That has been playing on him, sometimes players can't find form either. These things can weigh heavy on you. Sometimes mentally you can get dragged down."