NEW: Trump suggests Hassett will not be his pick for Fed chair. Trump started his health care event by praising Hassett’s TV appearance this morning. Then says, “I actually want to keep you where you are.” Then adds, “we don’t want to lose him, Susie.”

From our story last night: "...the president recently indicated to advisers that he might prefer keeping Hassett in his current post because he likes how Hassett defends his policies on television..."