Maxwell confirmed that the national stadium is to remain the home of Scottish football but conceded that improvements are needed.
The governing body had been considering taking major internationals and Scottish Cup semi-finals and finals to Edinburgh following an offer from the Scottish Rugby Union.
However, a £5 million deal to sell their stadium to the SFA has been struck with Ladbrokes League Two side Queen’s Park, who have owned Hampden Park since it was opened in 1903.
Maxwell is aware of the widespread criticism of the stadium as a football venue with the huge distance between the pitch and seats behind each goal a common complaint.
German outfit Stuttgart solved a similar problem at their stadium, in part, by building two new stands at each end amid a radical refurbishment and according to Maxwell, there is the, “possibility of that happening” at Hampden Park.
He said: “We are aware of the Stuttgart model, they have brought the ends in and that is something that we are absolutely committed to investigating as part of the wider development of the stadium.
“We need to speak to them, take advice from them and look at other areas of innovation that are around to see what we can do to enhance the stadium atmosphere.
“There is no doubt that Hampden needs to be improved. We are not going to hide from that, I am not going to hide from that.
“Whether that is outside the stadium in terms what we can do to enhance the pre-match experience, what we can do inside the stadium, what we can do from a seating perspective, this is very much part of a journey for the Scottish FA to make the Scottish national stadium the best it can possibly be and we are committed to doing that.”