Football Association chief executive Brian Barwick has backed Uefa's plans for domestic cup winners to qualify for the Champions League.
Platini has his own plans for the Champions League
Uefa president Michel Platini's may be on a collision course with the Premier League, who want to keep four places.
Barwick told BBC Radio 5live: "It is important to keep as many English clubs in the Champions League as possible.
"If another route is via the FA Cup, it's a perfectly reasonable suggestion. It might get other clubs into it."
In the last 10 years the FA Cup has only been won by the clubs that finished in the top four last season - Manchester United, Arsenal, Liverpool and Chelsea.
However, Barwick said the possibility was there to open qualification up to other clubs.
Referring to West Ham's last-gasp defeat in the 2006 FA Cup final by Liverpool, Barwick added: "West Ham were a minute away off having qualified."
Uefa's executive committee will decide on Platini's proposals in November.
His controversial proposals would also see six places in the Champions League reserved for champions of the 40 lowest leagues in Uefa's 50 member countries.
The champions of the top 12 associations will automatically qualify for the group stage.