Pickford has endured a difficult start to the season, with the Toffees having lost all four league matches so far this season and rooted to the bottom.
The England No1 has now conceded 13 goals this term after Everton dropped a two-goal lead once again to lose 3-2 against Aston Villa.
According to The Sun, Dyche is unhappy with Pickford's displays, with the shot stopper under huge scrutiny.
Dyche is said to be ready to make changes between the sticks in January if the current situation doesn't change.
Sean Dyche is reportedly ready to axe Jordan Pickford if his poor form doesn't improve
The same outlet claims he will make a move for Newcastle's Nick Pope in January should Pickford's performances not improve.
Dyche knows Pope well having managed him during their time together at Burnley and his name is dropped whenever the former criticises Pickford.
Pope could be made available for transfer by Newcastle, with the Magpies keen on Burnley's James trafford as a long-term replacement.
Mail Sport reported in June that the Newcastle had unsuccessfully tabled an offer of around £16million for the 21-year-old.
Pickford has been Everton's first choice goalkeeper since he joined from Sunderland for £30m in 2017 but his long reign could soon come to an end.
The 30-year-old's poor form was on display last month when he took a heavy touch before being closed down by Son Heung-min, who guided the ball into an empty net as Tottenham thrashed Everton 4-0.
Since his Everton debut seven years ago, Pickford has made 284 appearances across all competition, keeping 77 clean sheets in that time.