Captain Deeney has been linked with a move to Arsenal in recent days but has distanced himself from the rumours while the club’s leading goalscorer Ighalo has stated it is his “dream” to one day play for Manchester United.
Both have been in fine form for the Hornets this season as Flores has guided the promoted side to ninth in the Premier League table.
They host strugglers Newcastle in the FA Cup third round tomorrow and, while Ighalo or Deeney may yet be rested for the clash with Steve McClaren’s side, Flores has moved to deny all speculation linking the pair with a January departure.
“I think it’s completely impossible,” the Spaniard said when asked if there was any possibility either player would be sold.
“Our target as a team is very clear. The confidence of these players is amazing. They are completely confident in themselves.
“They are not in a hurry or a rush to leave Watford. They’re happy at Watford. It’s important to value these kinds of things — how important it is to be happy in a place.”
However, Flores, while insisting that neither striker will be sold in January, did admit his star duo may look to move on at the end of the season.
“It’s something you need to accept,” he said. “When? I don’t know. It’s possible someday you’ll lose these players.”
Meanwhile, Ronald Koeman has vowed to let Sadio Mane and Victor Wanyama sit “in the stands” if either star agitates for a move from Southampton.
Manager Koeman has again insisted that both Mane and Wanyama will remain at Southampton beyond the January transfer window, despite strong interest from Premier League rivals.
Koeman dropped Mane for Saturday’s 1-0 league defeat at Norwich after the Senegal forward was late for a team meeting, sparking fresh speculation he was headed for a January transfer.
The Saints’ Dutch boss continues to reject all suggestions either Mane or Wanyama are itching for a move — and vowed to banish anyone misbehaving in order to force a transfer.
“If there is any player thinking if his behaviour is not good that makes it more easier for the player, then I’ll put the player in the stands until the end of their contract,” said Koeman.
“Because in my opinion that’s not the way you have to do your job as a football player.”
In other transfer news, Sunderland boss Sam Allardyce has made Bayern Munich defender Jan Kirchhoff his first signing of the winter transfer window.
The centre-back has agreed an 18-month deal for a fee understood to be in the region of £750,000 (€1m).
Everton have signed Switzerland U21 forward Shani Tarashaj on a four-and-a-half-year deal.
The 20-year-old joins from Grasshoppers and will be loaned back to the Zurich club for the remainder of the 2015-16 season.
No fee was announced by Everton but it has been reported as being £3m (€4m).
Elsewhere, Coventry have signed Joe Cole on a free transfer from Aston Villa while Brighton have completed the signing of former Leicester winger Anthony Knockaert from Standard Liege for an undisclosed fee.