Despite losing 3-2 at Ross County on Saturday after taking a two-goal lead, the Hoops are still 15 points clear of Motherwell at the top of the table and cruising to their second successive title.
While Neil Lennon's men were lavished with praise for reaching the last 16 of the Champions League, many believe Celtic have been affected in the league by the absence of their old Govan rivals who languish in the Irn-Bru Third Division, where they re-emerged this season after falling into administration and then liquidation.
Mulgrew was at Hampden on Monday to promote PFA Scotland's player-of-the-year awards event, yards from where talks about the rule book for proposed league reconstruction were taking place between SPL clubs.
Asked if was down to him, would he have Rangers back in the SPL, the Celtic defender said: "If it was my choice? Probably, yes.
"I don't want to get involved in what is going on that side of things, I am just concentrating on things at Celtic and hopefully things will work out for the best."
The Scotland defender then addressed the notion that the Celtic players have subconsciously, if intermittently, let their guard down this season due to the loss of the Ibrox club from the top flight.
"It is hard to say," said Mulgrew, who was both PFA Scotland and the Scottish Football Writers' player of the year in 2012.
"There is not as much pressure on you but I am not using that as an excuse.
"The players know we weren't good enough against Ross County on Saturday and the performance was not acceptable.
"We should have gone on and won that game after being 2-0 up but we never so we have to look at that and hopefully will be ready when the next game comes.
"We just know we have to do better.
"At a team like Celtic there should never be a lack of motivation.
"The fans demand and the club demands that we win every match.
"So it's not a lack of motivation, it's just that we have to do better. It is simply that.
"It has been a good season for us, we got to the last-16 of the Champions League when nobody gave us a chance.
"We have had a couple of disappointing results but the main thing is we win the league.
"It doesn't matter how much we win it by, as long as we win it and we are also in the Scottish Cup so we will look to do as best we can in that as well."
After the Dingwall defeat Lennon said that some of his players were perhaps looking at life away from Parkhead.
However, the former Aberdeen player said: "Everybody is focused on the job ahead at Celtic, all the players are focused on what they have to do.
"So I don't think people's heads are elsewhere. I just think it was a bad performance and we have to look to rectify that in the next match."
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