The Yankees would certainly have some company in their pursuit of Kuroda, as in the same tweet, Heyman noted that the Red Sox have let the Dodgers know they are interested as well. We do know that the Yankees are more inclined to go after rental starting pitchers, as Kuroda would be, rather than spend lots in prospects to land a more long-term solution.
There is also one other possible snag in any deal the Yankees could make for Kuroda: He has a full no-trade clause and has indicated that he would need some form of compensation to waive it. That could mean that he is looking for an extension from any team looking to deal for him.
If that turns out to be the case, it could mean the Yankees won’t go after him as hard as they otherwise would, again, preferring rental starters. Kuroda is 36 years old, after all. Getting him past this season might not be the smartest idea, depending on the money.