The market for Dodgers right-hander Hiroki Kuroda is growing. The question of which teams he would approve for a trade – if any – remains unclear.

The Yankees have intensified their pursuit of Kuroda, according to major-league sources, and the Red Sox also are in the mix along with the Rangers, Indians and Tigers.

Kuroda, who has a full no-trade clause, is leaving all of his options open, and will weigh each trade possibility on a case-by-case basis, a source said last weekend.

The Dodgers have yet to present him with a formal proposal to accept or reject. However, speculation persists that Kuroda will approve a trade to only certain clubs – and perhaps only the Yankees and Red Sox.

Both clubs face rotation concerns. Kuroda is owed the balance of his $12 million contract – approximately $4 million – and will be a free agent at the end of the season.

-Ken Rosenthal and Jon Paul Morosi