While Chelsea manager Jose Mourinho has ruled out the historic prospect at such an early stage of the season, there is growing belief his squad is strong enough to finish the season unbeaten, thus emulating Arsenal's unbeaten season of 2003/2004.
If they avoid defeat tomorrow, they will be a quarter of the way to achieving the feat, with British bookmakers rating it still as a 10-1 shot.
The return of Costa, who has nine goals this season, from injury after a four-match absence also makes Chelsea 7-1 favourites to score the fastest goal in the Premier League this weekend.
At the other end of the table, Burnley have not won in their opening nine league games and as they approach a visit to Arsenal on Saturday, the odds are 2-1 for Sean Dyche's side to beat QPR's unenviable Premier League record of 17 games from the start of the season without a win.
Liverpool travel to Newcastle looking to overcome an indifferent league start with captain Steven Gerrard admitting this could be his last campaign for the Anfield club.
The 34-year-old's current deal expires at the end of the season and should he leave, an Asian club are favourites to sign him at 7/2, with a move to a Major League Soccer club in the United States at 5/1 and a deal with another Premier League club 14/1.