The last sentence could be interpreted as a reference to Paul’s longtime relationship with his star client — LeBron James of the Los Angeles Lakers — since the Lakers have been considered the league’s most ardent suitor for Davis for months.

Davis also faces possible league discipline because the N.B.A. typically fines players when they, or their representatives, publicly request a trade.

“We commenced an investigation this morning upon reading the reports regarding Anthony Davis,” the N.B.A. spokesman Mike Bass said Monday. “That process is ongoing.”

Teams such as the Knicks and Davis’s hometown Chicago Bulls are among the many clubs expected to join the Lakers in pursuing a trade for Davis over the days leading to the 3 p.m. trade deadline on Feb. 7. Yet it might behoove New Orleans to wait until closer to the draft to get serious about dealing its franchise player.

That is because the Boston Celtics, regarded for some time as the Lakers’ foremost challenger in the long-anticipated trade sweepstakes for Davis, are ineligible to acquire Davis via trade while the All-Star guard Kyrie Irving is on Boston’s roster. League rules preclude one team from having two players on the designated rookie scale contract extensions possessed by both Davis and Irving.

With a record of 22-28 in a season marred by numerous injuries, New Orleans had slipped to 13th in the Western Conference entering Monday’s play and looked increasingly unlikely to make a playoff run. The Pelicans, though, are under no obligation to trade Davis and could decide to wait until after the season, when the Celtics would be able to join the bidding. Irving has the ability to become a free agent on July 1 by declining the $21.3 million player option he holds for next season.

Knicks Coach David Fizdale tried to downplay his team’s interest in Davis on Monday. But the Knicks — who were already planning to make a free-agent run in July at the likes of Kevin Durant and Irving — could emerge as a team to watch for Davis if they show a willingness to make trade assets such as the star forward Kristaps Porzingis, their prized rookie Kevin Knox and this June’s likely top-five draft pick part of any discussions.

Although Davis has missed the Pelicans’ last four games with a finger injury, Coach Alvin Gentry told reporters Monday that he expects Davis back in the lineup soon. Davis, according to Gentry, plans to play out the season even if New Orleans elects to keep him past next week’s trade deadline.