The Toffees kicked off the Allardyce era with a 2-0 home win over Huddersfield Town on Saturday afternoon, with Gylfi Sigurdsson and Dominic Calvert-Lewin found the net to earn Allardyce all three points.
Despite starting with a win, Allardyce will almost certainly be using the next month to analyse his squad and plot potential signings in the January transfer window.
ESPN now report that Allardyce has made Watford striker Troy Deeney a top target for the January window, with the new Everton boss keen to bring in another striker.
Everton failed to replace Romelu Lukaku following his big-money summer move to Manchester United, and Allardyce is unsurprisingly looking for a proven centre forward to lead the line.
Deeney, 29, fits the bill given that he has scored 108 goals in 313 games for Watford, captaining the side whilst becoming a firm fan favourite at Vicarage Road since a 2010 move from Walsall.
A burly striker with great work rate and strength, Deeney has been in and out of the Watford side this season following the signature of Andre Gray, starting just four Premier League games.
It now seems that Deeney is a top target for Allardyce, and he will look to capitalise on his lack of regular starts by offering him a big move to Goodison Park in January.