[Update 6/7/17: It is being reported that Trump has been furious at Jeff Sessions that Sessions recused himself from Russia investigation matters, and, as a consequence, Sessions offered to resign. All that, it seems to me, shows some spine by Jeff Sessions. Luther Strange, former Alabama state Attorney General, could show some spine by opining one way or the other whether he thinks Sessions was right to recuse himself.]
The information at this time is that President Trump does not think Jeff Sessions should recuse himself. See Boston Globe and Breitbart.
The question of recusal deals with conflicts of interest, how the law looks at conflicts of interest, and what government officials should do in situations of conflicts of interest.
Since November there has been pressed on President Trump that his businesses present serious conflicts of interest for him, and that what he says he is going to do with his businesses is not adequate in dealing with his conflicts of interest. President Trump says conflicts of interest are not applicable to him as President, and he is exempt from or above conflicts of interest standards that apply to other government officials. The position that President Trump is taking on his business interests is being contested and will continue to be tested in various ways in the coming months, and the ultimate outcome remains to be seen.
The mentality that President Trump has that conflicts of interest do not apply to him seems to be carrying over to Jeff Sessions, and is starting to evidence a pattern and a belief by President Trump that the law does not apply to him, and he is above the law, and further the law does not apply to anyone President Trump decides the law should not apply to, such as to Jeff Sessions.
President Trump's saying that Jeff Sessions should not recuse himself is further grounds for Congress to censure President Trump.
Edit: The Wall Street Journal is reporting today Donald Trump Jr. Was Likely Paid at Least $50,000 for Event Held by Hosts Allied With Russia on Syria. The subheadline says,
"October appearance by son of then-candidate is one of string of contacts between members of the president’s inner circle and individuals connected to Moscow". This seems like exactly the "pay to play" that Trump crucified the Clintons about during the campaign. We'll have to await to hear whether President Trump says "conflicts of interest" and "pay to play" do not apply to him and his family.