Vardy nets both goals in a 2-0 home win for the top-flight leaders as Arsenal are leapfrogged by Tottenham.
Italian boss wants a new striker amid links with Chelsea star Loic Remy and Crystal Palace's Dwight Gayle.
The 20-year-old star has joined the Blues on four-and-a-half-year contract.
The 26-year-old striker has not appeared for the Anfield club since early December.
Nigerian striker Ahmed Musa has scored 10 goals in 29 appearances for CSKA Moscow this season.
Liverpool along with Arsenal and Tottenham are chasing the signature of Leicester City youngster Ben Chilwell.
Leicester City are hoping to ward off interest for Chilwell from Arsenal and Tottenham with an improved contract.
Van Gaal is wary of letting too many players leave on a permanent or temporary basis midway through the season.
Claudio Ranieri is unwilling to sell any of his top stars this summer as he moves for the title.
Mark Schwarzer says the Reds will have to wait until the summer to launch Foxes stopper bid.
Mark Schwarzer believes Jose Mourinho will take Manchester United a long way forward.
Vincent Kompany will be out for at least another month with a calf injury, confirms Pellegrini.
Ben Chilwell is yet to make an appearance in the Premier League for Leicester City.
West Ham have beaten both Arsenal and Manchester City this term.
Ranieri says they are second in the league because traditional big teams are not at the top of their game.
26-year-old Nigerian is delighted by the Foxes' attention-grabbing results this season.
Leicester City take on Tottenham Hotspur in the third round replay of the FA Cup. Find out where to watch the game live in the UK.
Leicester scout Ben Wrigglesworth played a key role in bringing Mahrez and Kante to the King Power stadium.
Ranieri remained coy on suggestions that Daniel Amartey has agreed a move from FC Copenhagen.
The Foxes lie second in the Premier League table, behind Arsenal on goal difference.
Algeria's Islam Slimani has scored 13 goals in 16 league games for Sporting Lisbon thus far this campaign.
Robert Huth's late header gave the Foxes a 0-1 victory at White Hart Lane.