Spurs have lost just one of their last 14 top-flight fixtures to reignite hopes they can catch their London rivals during the run-in.
Antonio Conte's side remain in a commanding position but the pressure on the Blues will be ramped up if they lose tonight's clash with Manchester City.
Pochettino has appeared to be publicly downplay his team's chances of pipping Chelsea at the post but Carroll, who played for the Argentine coach before joining Swansea in January, believes the message in private may be different.
"Knowing the manager there I am sure he will be telling the lads the title race is very much on," Carroll told ITV.
"Last year was a good year for them, they were close and they have top-class players.
"They are one of the teams who are good enough to be knocking on the door every year.
"Ideally, we would take three points off them - because that is the most important thing for me - and then they go on and win it."
Carroll has thrived since moving to South Wales on a permanent basis, having rarely been afforded regular game time at White Hart Lane.
Swans manager Paul Clement believes the midfielder has a "point to prove" against his former employers and Carroll is convinced an upset could be on the cards at the Liberty Stadium.
"They are pushing for the title and we are fighting ourselves. Anything can happen at this time of year.
"We have seen a fair few times that the sides at the top of the table can be upset, and we will be looking to do that ourselves having done it against Liverpool," added the 24-year-old.