Manchester City have reportedly denied they will move for these two strikers.
Vardy has taken the Premier League by storm this season as his goalscoring exploits - where he broke a league record by scoring in 11 consecutive games - has helped the Foxes to the summit of the division this season.
As a result there has been speculation that the league's joint leading scorer with 15 goals could be the subject of interest from the league's more illustrious and wealthier clubs.
City have the biggest spending power in the league and as a result would have the capacity to lure Neymar from current European Champions Barcelona, as well as keeping him at the Champions League level but it could be seen as a step down for the Brazilian who is with a side which has an impressive record in the competition over the last 10 years - having only failed to reach the semi-finals of the competition on two occasions in that time.
It would take some offer for City to even turn the head of Neymar who is currently playing with what is regarded by many as the best strike force in the World alongside Luis Suarez and Lionel Messi.
As a result it is probably of little surprise that City have ruled out that particular move.
But one thing the report does note is that City last season ruled out a move for Wilfried Bony when he was at Swansea City, only to sign the Ivory Coast striker in the January transfer window.
Sergio Aguero has had his share of injury problems again this season, while some haven't been convinced by Bony even though he has chipped in with a few goals, while Manuel Pellegrini opts for Kelechi Iheanacho as his third forward.
There is the chance that another forward may arrive at the Etihad Stadium, just not Neymar or Vardy.