Cardozo had looked on course to complete a move to Fenerbahce earlier this week, before it fell through due to the Portuguese club's asking price.
That could see either Premier League side step in for the Paraguayan international, but according to talkSPORT, Fenerbahce president Aziz Yildirim is prepared to wait to see if Cardozo's asking price is met.
Yildirim said: "Let's see if we can find a club that will pay £14.5m.
"Wait until the first week of July. Cardozo is a great player, but we have to consider the interests of the club, and see if there is a club who will pay £14.5m for a 30-year-old."
Cardozo scored 33 goals for Benfica last season.