While Liverpool fans will be disappointed to miss out on a chance to view their new record signing, Rush believes the former Auxerre man will be rearing to go for the Reds after a summer break.
Rush said: "Liverpool supporters will be disappointed they're not going to get a glimpse of Djibril Cisse in Euro 2004. I'm quite happy he won't be playing.
"I feel sorry for Cisse because it would be a great experience for him to play in a major tournament. But, by the time pre-season comes along, he will be desperate to get going.
"I didn't play in a World Cup or European Championship for Wales so I know what it's like to have a rest over the summer. It usually drives you mad to go two weeks without a match, so by the time six weeks have passed you will do anything to kick a ball. Cisse will feel that way in July and Liverpool will reap the benefits.
"Apart from that, could you imagine what would have happened if Cisse had scored a bagful in Portugal? Chelsea would probably have offered £28m for him and tried to hijack the deal before he arrived on July 1!"