The Blues are also hoping to land Bayer Leverkusen playmaker Kai Havertz.
Lampard is clearly bolstering his front line at Stamford Bridge, however, the Blues boss is also hoping to replace Arrizabalaga.
The former Chelsea star has ran out of patience with the £71m goalkeeper, who has struggled to impress in west London.
Chelsea news: Frank Lampard is ready to splash the cash
And according to the Daily Mirror, Chelsea are going to up their interest in Burnley No. 1 Pope
They say Lampard has made the 28-year-old his top goalkeeper target now the transfer window is open.
England international Pope still has three years remaining on his contract at Turf Moor.
However, it’s understood a bid of £50m could tempt Sean Dyche to sell the stopper.
It’s claimed Pope is keen to join one of the Premier League big boys in the transfer window to boost his England chances.
Pope wants to usurp Everton’s Jordan Pickford as Gareth Southgate’s first choice ahead of the European championships next summer.
Pundit Jamie Carragher has backed Lampard’s move for a new goalkeeper, with the Liverpool hero claiming Chelsea need a new stopper and a couple of defenders.
“Chelsea won’t go any further unless they change their goalkeeper,” Carragher said.
“Going back to how important goalkeepers are, I look at this Chelsea team and there’s a lot I like about it, it does remind me in a lot of ways the position Jurgen Klopp was in a couple of years ago.
“He’s done as much as he can, yes Frank’s still in his early stages but those big signings can completely transform you as a team.