Lampard will coach Everton, according to Romano, and the two sides have reached an agreement.
Everton sacked Benitez this month and the Toffees are currently led temporarily by assistant coach Duncan Ferguson while the club is looking for an official manager.
According to Romano, Everton have now chosen Lampard to take over the team, the two sides have negotiated an agreement, and official announcements will soon arrive.
Lampard, who previously coached Derby County and Chelsea, has been idle since he left the Blues last January.