Kyrie Irving appears to be laying the ground work to leave the Brooklyn Nets this summer.
Irving has until June 29 to decide if he wants to exercise his $36.9 million player option for next season. He has been discussing a new contract with the Nets as that deadline looms. According to ESPN’s Adrian Wojnarowski, Irving has given the Nets a list of teams he would like to be traded to if the two sides cannot work out a new deal.
ESPN Sources: If Kyrie Irving can’t reach an agreement to stay with Brooklyn, he has a list of teams he’d like them to consider on sign-and-trades, including Lakers, Clippers, Knicks, Heat, Mavs and 76ers. None of those teams have cap space to sign him without Nets’ help.
— Adrian Wojnarowski (@wojespn) June 23, 2022

That does not necessarily mean Irving will leave Brooklyn, but it certainly is an indication that he is open to it. If he does want to play for another team, the Nets would rather get something of value in return. That is why they would likely want to have Irving opt in to facilitate a sign-and-trade.
As Wojnarowski noted, none of the teams Irving would be interested in playing for have enough salary cap space to sign Kyrie as a free agent. That is another reason a sign-and-trade would make sense.
A separate report on Thursday claimed Kevin Durant is also weighing options for his future. Durant is under contract with the Nets through the 2025-26 season, but he probably would want a fresh start elsewhere if Irving leaves.
It is also entirely possible that Irving and Durant are trying to put pressure on the Nets. The Nets are said to be hesitant to sign Kyrie to a long-term deal because of all the drama surrounding him in recent years. Perhaps Durant is trying to give his close friend an assist by helping Irving secure a new contract.