The pair admit that it will be special for the veteran manager to take club clear of bitter rivals with 19th title, a feat that would make lifting the trophy sweeter for fans
The Scot has gone on record as saying it was his ambition to knock the Merseysiders off their perch when he took charge of the club in 1986 and he has since won 11 titles, with the Anfield outfit not adding to their tally since 1990.
Now with both clubs locked at 18 titles each, United would overtake Kenny Dalglish's men if they win the league this season.
"It would be amazing for the players and a great feeling for fans," Brown told Inside United.
"But, for me personally, I'd be really pleased for the manager. For him to take us past their record would be brilliant."
Carrick maintained that a league triumph this season would hold a special place among all the others that the team have won in recent years.
"This one would definitely be pretty special," he said. "The others are special in their own right, but for everyone at the club and the fans this one would have that little bit more meaning."