His reign ended in acrimonious circumstances in November 2004 after a decline in his relationship with Baggies chairman Jeremy Peace.
But Mowbray believes Megson, who had spells in charge of Nottingham Forest and Leicester before moving to the Reebok Stadium, deserves credit for his achievements at West Brom.
He said: "I would like to think he would get a very positive response. He achieved two promotions to the Premier League with this club. That is a wonderful achievement.
"I would hope the supporters show their appreciation of the good times Gary Megson had at the football club - but then, once the game gets rolling, I am sure they will be firmly behind West Brom."
It is the Baggies fans that Mowbray cannot praise highly enough for the way they have stayed positive towards the team this season despite being bottom of the table.
He said: "It is great credit to the fans. With our current predicament, many, many fans would have turned by now against their team - particularly with the nature of the goals we have conceded when we have been very competitive in games.
"It has punctured the atmosphere in the stadium at times and it is great credit to the fans that they have stuck with the team. Hopefully they will continue to stick with us and we can reward them by getting the victories we all want.
"I have no idea why they are so positive. I would assume through history they have got a reputation of being positive and supportive of their side. That is fantastic and long many it continue."
Mowbray knows his players also have to play their part in maintaining the rapport with supporters and is confident the next two games - at home to Bolton and Stoke - can give them a platform for a late revival.
He said: "Can we turn it around? Within the ranks, the players think that and on the terraces. We need to get the results to keep motivating the fans to stick with the team.
"The team genuinely believe these next couple of games will give us the platform to push on and get the required wins to stay in the division.
"We have to go and do it on the field and get the job done."
Mowbray is hoping Monday's goalless draw at West Ham will prove to be a launchpad for an 11th hour attempt to survive in the top flight after admitting his side have lacked the necessary qualities in some departments this season.
He said: "It is very difficult, in the short period of time you get, to get all the ingredients right and ultimately we haven't got the ingredients all right this season.
"A football team is made up of all components, the ability to defend, attack, create and destroy. We haven't had all those components in place.
"Yet I sit on the touchline most weeks and say 'I am proud they are my team.' I enjoy watching them, the quality they show, the bravery they show going away and taking teams on and playing football.
"I think it is the way forward. We aren't too far away from being a very competitive team, even in the top half of the Premier League - if we can survive this year and get the right couple of players in.
"I don't want to play survival football year in and year out, hoping to finish fourth bottom."
Albion will again be without central defenders Leon Barnett (knee) and former Bolton player Abdoulaye Meite (hamstring) in addition to long term injury victims Ishmael Miller and Neil Clement.