Lampard took over at Goodison Park on Monday, replacing Rafael Benitez at the helm.
The ex-Derby County boss has assembled a backroom staff to support him in his new stint on Merseyside, which includes the likes of Joe Edwards, Chris Jones, Paul Clement, Duncan Ferguson and Alan Kelly.
Lampard is also mulling over roping in his former Chelsea team-mate Cole to help him in a first team coaching role.
The 41-year-old is currently assistant to Lee Carsley for the England Under-21s.
However, even if Cole joins Lampard’s staff, he will not relinquish his position in the England youth set-up.
Cole is expected to combine his current job with his duties at Everton, provided he links up with his former Blues team-mate at Goodison Park.
It remains to be seen whether Cole will answer Lampard’s call and help him get the Toffees’ season back on track.
