Premier League leaders United currently hold a four-point advantage and a game in hand on Hiddink’s side.
But the Dutchman claims the Blues will not give up on the title — even if it appears destined to remain at Old Trafford.
He said: “The task we are facing is extremely difficult.
“Don’t forget that Manchester have a game in hand and, moreover, they have a lot of experience of winning the league.
“But all I can promise is that Chelsea will fight to the bitter end.”
Hiddink has already guided the Blues to four Premier League wins since replacing Phil Scolari.
And Russia’s national coach insists his methods have been fully embraced by his Chelsea players.
He added: “Everybody knows my way — work, work and more work.
“That has been the principle since my first day in London and so far it is working.
“We started in fourth place in the Premier League, now we are second.”