The Clarets started the season with their customary 40-point target and safety in the Premier League but things have gone so well some are dreaming of higher things.
Europe is on the lips of some fans as they sit in seventh place in the Premier League ahead of the hectic Christmas schedule but Bardsley is urging caution.
The 32-year-old told the Burnley Express: “It’s for the fans to dream. They pay a lot of money to travel up and down the country week in and week out and they deserve to have a sniff.
“Let’s not get carried away too early, there’s still a long way to go, the Christmas period is vital with a lot of games, if we keep performing like we have been, we’ll pick up more points.
“The manager has drilled it into the lads over the last four of five years what he wants.
“You can see the club is growing, players are improving and everyone wants to get the club as high as possible.”
Watford boss Javi Gracia does not think Abdoulaye Doucoure's form will be affected by his omission from France's latest squad.