WASHINGTON—President Donald Trump’s lawyers are seeking to negotiate a deal with special counsel Robert Mueller that uses an interview with the president as leverage to spur a conclusion to the Russia investigation, according to a person familiar with the discussions.

The president’s legal team is considering telling Mr. Mueller that Mr. Trump would agree to a sit-down interview based on multiple considerations, including that the special counsel commit to a date for concluding at least the Trump-related portion of the investigation....