The Robins have taken seven points from a possible nine since Millen took over first-team affairs following Gary Johnson's departure earlier this month.
Lansdown will now step up his search for a permanent successor to Johnson but he insists the job Millen has done has not gone unnoticed.
"We're beginning to talk to people now and make enquiries for those people we feel could do a job for us. Keith Millen is one of those people," Lansdown told the club's official website.
"What I've discussed with Keith is that I want him to know he will be in charge at least until the Scunthorpe match (April 17). That's four more games and by that time hopefully we will have done all our talking and examination of applicants. Then we should be in a position to decide who will be the next manager of Bristol City.
"That would give the new incumbent a couple of games at the end of the season to assess the squad and be in a position to sort out the retained list as well as look at what we need for next season."