Here's who top conservatives and allies of the president want to see Trump pick for his next nominee: 
 
 Mitch McConnell Addison (Mitch) Mitchell McConnellSupreme Court fight becomes battle for Kavanaugh’s papers GOP senator warns against 'fishing expedition' for Kavanaugh documents It’s time we start thinking about post-Trump America MORE (R-Ky.): Raymond Kethledge and Thomas Hardiman 
 
 Though he hasn't backed anyone outright, the Senate Majority Leader is reportedly nudging Trump toward nominating Kethledge or Thomas Hardiman, because they present "the fewest obvious obstacles to being confirmed," The New York Times reported Saturday. While careful not to directly make the case for any would-be justice, Mr. McConnell made clear in multiple phone calls with Mr. Trump and the White House counsel, Donald F. McGahn II, that the lengthy paper trail of another top contender, Judge Brett M. Kavanaugh, would pose difficulties for his confirmation. Mr. McConnell is concerned about the volume of the documents that Judge Kavanaugh has created in his 12 years on the United States Court of Appeals for the District of Columbia Circuit, as well as in his roles as White House staff secretary under President George W. Bush and assistant to Kenneth W. Starr, the independent counsel who investigated President Bill Clinton.
– Mitch McConnell has been calling the White House daily, and not to discuss President Trump's golf game. McConnell has been carefully explaining—without explicitly telling Trump what to do—which Supreme Court nominees would get faster approval before the November elections arrive and make everything dicey, insiders tell the New York Times. McConnell prefers Raymond Kethledge and Thomas Hardiman and warns that reported front-runner Brett Kavanaugh poses two problems: too long a paper trail from his 12 years on the US Court of Appeals for the District of Columbia Circuit, and too much political baggage from his years as assistant to Kenneth Starr and staff secretary to President George W. Bush. McConnell has also told Trump he could lose two Senate votes (Lisa Murkowski and Susan Collins) with another apparent contender, Amy Coney Barrett, who has trumpeted socially conservative views and may be more likely to overturn Roe v. Wade. McConnell is also aware that with John McCain away fighting brain cancer, the GOP has only 50 votes, and libertarian-leaning Rand Paul could be a wild card. The Times describes Kethledge as a "strongly conservative" Midwesterner who hasn't spent much time in Washington, and Hardiman as a "reliable conservative" who served with Judge Maryanne Trump Barry, one of Trump's sisters, on the federal appeals court in Philadelphia. Check out the Hill to see which contenders are being pushed by other top conservatives.