The former England captain’s present deal expires in December and the RFU, under previous chief executive John Steele, opted to leave negotiations until the tournament in New Zealand finishes.
After leading England to their first Six Nations title in eight years, Johnson hinted he would like to continue in a job the role.
If Johnson still feels the same after the World Cup, then Thomas would welcome the chance to sit down and discuss the future with him.
“Martin is such an honest assessor of his own performance that he will judge himself after the World Cup,” said Thomas, who has stood down as RFU chairman but will run the day-to-day union affairs until the new year.
“He will turn around and say he is pleased with what he has done and he is staying or that, because he is very self-critical, that he is not happy.
“There is unlikely to be a CEO before January. I will have no problem in sitting down with Martin after the World Cup and resolving his position in the interests of England and the coaching team.”