The Toffees are deep in trouble in the Premier League and their situation got no better on Saturday when they lost away at West Ham United.
Fans are deeply unhappy with the way the club is being run and Lampard is under pressure to turn things around.
Arnaut Danjuma is set to join Everton on loan from Villarreal, but Lampard wants more attacking power and is looking to Stamford Bridge.
He holds an interest in signing Chelsea winger Ziyech.
The Morocco international has struggled for game time at Chelsea this season and has been linked with a possible exit.
Everton would want Ziyech on an initial loan deal.
Whether Chelsea, who has splashed the cash on new additions and may want to bring some in, will be prepared to loan Ziyech out, remains to be seen.
The winger also has interest from other clubs beyond Everton.