Gary Cohn is the current Chairman of the President’s Economic Advisors and is supported by the establishment Republicans. With a long career at Goldman Sachs, he is probably too stained to be appointed, despite his other impressive qualifications. Or, those establishment Republicans could content themselves with Kevin Warsh, who is very young and unproven but has already served a partial term as a Fed Governor under a Republican administration.
Democrats would be most content with the reappointment of Janet Yellen or current Fed Governor Jerome Powell, who are less likely to raise rates quickly. Democrats also know their opinion doesn’t matter on this.
The President is a real estate developer, who are generally heavy borrowers and therefore prefer lower interest rates. Besides, increasing interest rates will increase the cost of carrying our $20 trillion of government bonds, which takes money away from other Trump priorities. It also decreases consumer spending by voters. I would not be surprised if the President supports the Democrats on this important appointment and appoints either Yellen or Powell. If so, expect little disruption in the credit markets.