Linfield manager David Jeffrey says the champions will not be giving up their title chase "until it is mathematically impossible" to retain the Gibson Cup.
"No-one should be in any doubt that we are going after the league title - we're not giving up on anything," said Jeffrey ahead of Tuesday's game against leaders Cliftonville at Windsor Park.
The Blues, who now lie third, have William Murphy suspended for the match.
"If we don't win it's going to be very, very difficult to retain our title."
"Cliftonville have developed the knack of winning when they maybe haven't played particularly well, but this is a game we must win," said Jeffrey, whose side trail the Reds by 13 points and second-placed Crusaders by four.
Meanwhile Cliftonville boss Tommy Breslin has told his players that they must improve on their performance in Saturday's 2-0 win over Dungannon Swifts at Solitude.
Crusaders manager Stephen Baxter will check on the fitness of Josh Robinson and Timmy Adamson before his side's home game against Portadown, who have won their last two festive fixtures by a two-goal margin.
LIVE ON RADIO ULSTER
Michael McNamee will be at Windsor Park to cover the big match of the day between Linfield and Cliftonville for BBC Radio Ulster on New Year's Day.
He will be joined on commentary by regular analyst Chris Morgan.
Tuesday's Sportsound Special will be presented by Joel Taggart from 14:00 GMT and will also feature coverage of the other five games.
Former Lisburn Distillery manager Paul Kirk will offer his thoughts on the Crusaders-Portadown fixture at Seaview.
Robinson has suffered a fractured nose, while Adamson is struggling with an ankle problem.
The Ports have moved to within three points of sixth-placed Ballinamallard and will be boosted by the imminent arrival of ex-Shamrock Rovers striker Gary Twigg, who is not eligible to play on Tuesday.
Ballymena United will be without suspended midfielder Gavin Taggart for their trip to Stangmore Park to face Dungannon Swifts, following his dismissal against Lisburn Distillery on Saturday.
Sky Blues manager Glenn Ferguson will monitor the progress of central defenders Davy Munster and Aaron Stewart, who both retired hurt during the dramatic 3-3 draw with the Whites.
The United strikeforce will be bolstered by the arrival of former Carrick Rangers and Donegal Celtic forward Shane Dolan.
Donegal Celtic manager Pat McAllister has promised to make radical changes to his squad in the January transfer window as his side prepare to take on Glenavon at Suffolk Road.
Player-manager Gary Hamilton is struggling with a leg injury for the Lurgan Blues, while another striker, Matty Burrows, is leaving the Mourneview Park club to join Championship One side Ards.
Mark Farren comes in mid-season to offer Hamilton further options in his forward line, but Ciaran Martyn sits out the trip to DC because of an automatic one-game ban. Conor Hagan is back after a ban however.
Ballinamallard travel to face Lisburn Distillery having picked up just three points from their last five league encounters.
Distillery manager Tim McCann will hope for better after watching his side surrender a 3-0 lead to draw 3-3 at Ballymena, just days after being forced to accept a similar scoreline against fellow strugglers Donegal Celtic.
Aaron Traynor will be missing for the Whites due to suspension.
Coleraine will hope to recover from their weekend defeat at the hands of Portadown, when they take on Glentoran, who have Stephen McAlorum available for selection after suspension.
Irish Premiership - Tuesday 1 January - 15:00 GMT kick-offs
Coleraine v Glentoran
Crusaders v Portadown
Donegal Celtic v Glenavon
Dungannon Swifts v Ballymena United
Linfield v Cliftonville
Lisburn Distillery v Ballinamallard United