Carmelo Anthony tells reporters that it can be "mentally draining" to play through all the recent drama and trade rumors surrounding him. (1:12)

The New York Knicks and LA Clippers are searching for third-team facilitators to keep alive the prospect of completing a Carmelo Anthony trade, according to league sources.

Sources told ESPN that the Knicks continue to discuss the prospect of sending Anthony to Los Angeles without taking any of the Clippers' top three stars but have struggled to find a trade construction that works for both teams involving the other players on L.A.'s roster.

The most substantive talks between the teams took place last week, according to sources with knowledge of the discussions, but have continued into this week as the Clippers have maintained a consistent interest in Anthony, who has two years and roughly $53 million remaining on his contract.

The Knicks also have continued to try to assemble a workable trade that the Cleveland Cavaliers would consider for Anthony after ESPN first reported earlier this week that the Cavs rebuffed Anthony-for-Kevin Love proposals.

The recent thumb injury suffered by Anthony's good friend Chris Paul has complicated matters, with the Clippers reluctant to part with two of their healthy guards -- Jamal Crawford, Austin Rivers and J.J. Redick -- in any trade while Paul is sidelined.

Sources said the Knicks ‎are reluctant to absorb the three years and $42 million left on Crawford's contract after this season, which has led to the hunt for a third team that might be interested in Crawford. The Clippers, meanwhile, are hesitant to surrender the sharpshooting Redick even if they were at full strength in the backcourt, sources said.

Those various conflicting interests, sources said, have necessitated a search for a potential third team. Also complicating a potential Clippers-Knicks deal is the fact that L.A. is hard-capped this season, which would make it difficult for the club to handle the 15 percent trade kicker in Anthony's contract that would add nearly $10 million to his 2016-17 season if he is dealt.

Carmelo Anthony is one of only three players in the NBA with a full no-trade clause -- along with LeBron James and Dirk Nowitzki -- and has yet to fully sign off on any trade. Joe Robbins/Getty Images

The Clippers, sources said, have made it clear that they have no interest in surrendering Paul, All-Star center DeAndre Jordan or Blake Griffin in an Anthony trade, but they also couldn't trade Griffin to the Knicks even if they wanted to.

League rules, under the NBA's current labor agreement, prevent teams from trading for two players who were signed by their original team to a designated player maximum contract extension. The Knicks already have one such player on their roster in Derrick Rose.

Anthony is one of only three players in the league with a full no-trade clause -- along with LeBron James and Dirk Nowitzki -- and has yet to fully sign off on any trade. But the Knicks are purposely trying to engage in trade talks with teams that they believe Anthony would ultimately consent to joining, perhaps buoyed by the player's recent disclosure to Newsday that he would consider waiving the no-trade clause if the Knicks told him "they want to go in a different direction."

ESPN reported last week that Jackson met with Anthony and asked if he wanted to remain a Knick. Sources close to Anthony said he reaffirmed his desire to stay in New York at that meeting.

But both sides, sources said, left the meeting with an understanding that if Anthony were to provide a list of teams to the Knicks, they likely would begin soliciting offers.

The market for Anthony thus far has been tepid, sources said, partly due to the extremely limited number of teams it is believed he would be willing to join.

The Knicks also have tried to engage the Boston Celtics in Anthony talks, but sources indicate that those conversations haven't gained any traction because Boston feels Anthony doesn't address its need for more defense and rebounding.‎

Information from ESPN's Ohm Youngmisuk was used in this report.