Chelsea informed Kutner, after the club's 2-1 Premier League  win at Everton that there was no possibility of the midfielder staying at Stamford Bridge beyond the end of this season, the Telegraph reports.
Lampard originally learned of Chelsea's decision at last month's Club World Cup in Japan.
The England international could be in no doubt of owner Roman Abramovich's determination to let him go as the club reiterated their position last week, after a game in which he had scored two match-winning goals.
Kutner said Frank has had to accept the decision and just wants to carry on playing football for Chelsea, and wants to finish the season as successfully as possible for the club he loves.
Despite suggestions of recent dialogue between Lampard and the club, it is understood that these discussions were designed purely to appraise him of Chelsea's stance rather than to offer him any hope of a new deal.
Lampard moved alongside Kerry Dixon as Chelsea's second all-time leading scorer on 193 goals, which is nine behind Bobby Tambling, when he converted a penalty in Chelsea's 5-1 FA Cup third-round victory at Southampton. (ANI )