WASHINGTON—President Donald Trump’s legal team has submitted a counteroffer to special counsel Robert Mueller on a possible interview with the president that could allow for questions about collusion with Russia but curtail inquiries related to obstruction of justice.

As negotiations for such a sit-down are set to enter their eighth month, Rudy Giuliani, a lawyer for Mr. Trump, said Monday that an interview between the special counsel and the president is “still on the table.”

The...