Sen. Mike LeeDonald Trump has put a Utah senator at the top of his list of new potential Supreme Court picks. The Republican&rsquo;s response: Thanks, but no thanks.The Republican presidential nominee is set to release a list of 10 additional names he would consider to fill a vacancy on the high court. He first proposed potential picks&nbsp;after the death of Justice Antonin Scalia and the Senate&rsquo;s refusal to consider President Obama's&nbsp;nomination of Judge&nbsp;Merrick Garland to replace Scalia.According to NBC News, Sen. Mike Lee is among the new group, the only elected official on a list that includes appeals court, district court and state supreme court judges.Lee, who is seeking reelection this year and had endorsed Sen. Ted Cruz in the GOP primaries, has refused to back Trump. A spokesman sidestepped the question of whether Lee would accept the nomination if offered next year."Sen. Lee already has the job he wants, which is why he is campaigning to represent the great people of Utah again this year,&rdquo; spokesman Conn Carroll said.He added that the new list of potential justices, and his inclusion on it, &ldquo;does not change Sen Lee's mind about Trump in any way whatsoever.&rdquo;Trump put out an initial list of 11 potential picks in May, a move meant to offer reassurance to Republicans for whom the balance of the Supreme Court is a top priority. He said conservative groups such as the Heritage Foundation and Federalist Society helped draft the list.That initial list included another name that raised eyebrows: Diane Sykes, the former wife of a conservative radio host who has been an outspoken Trump critic. It also included Utah Supreme Court Justice Thomas Lee, the senator&rsquo;s brother.