Instead, the World Cup winner joined Italy's AC Milan in July on a three-year deal after his contract with Spanish club Barcelona was cancelled.
"I was offered Rivaldo six months ago," Al Fayed told reporters on Monday. "They contacted my managing director and he called me straight away.
"I didn't need to think at all about whether I wanted him, but he was too expensive for me.
"It would have cost 30 million pounds and I had to say no. Only very rich clubs could afford him.
"But I would love to sign him some time in the future if he was available for less."
Rivaldo was in London on Monday to visit Al Fayed's Harrods store for a publicity event.
The Egyptian presented the Brazilian international with a Fulham number 10 shirt with Rivaldo's name printed on the back.