The 28-year-old midfielder was voted the Toffees' player of the season and manager David Moyes has said he does not believe it is in Pienaar's best interests to leave Goodison Park.
But Ivan Modia told Sky Sports News: "At the moment it is unlikely that we can find a solution before the World Cup.
"He is very loyal to the club and it is up to what Everton want to do.
"To be honest he is really looking forward and hopes they can agree before the World Cup. If nothing happens before the World Cup with Everton we may have to consider other options.
"I am aware of the interest of some big clubs," Modia added.
Despite Modia's views Everton have said discussions with Pienaar, who has one-year left on his contract, are not likely to take place until mid-July when the World Cup has finished.