It is understood that there has been significant interest from both QPR and Sunderland, as well as number of other top-flight clubs in the Premier League and also across Europe.
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Cahill enjoyed a good World Cup for his country, becoming the first Australian ever to score in three successive tournaments, and netting one of the goals of the summer with a brilliant left-foot volley against Holland.
The 34-year-old, who scored 56 goals in 226 appearances for Everton, left England in 2012 for Major League Soccer side New York Red Bulls, for whom he was named Most Valuable Player after scoring 11 times.
Australia’s all-time leading goalscorer (34 times in 71 internationals) has settled well in the United States but it is believed he would consider a return to Europe if the right offer came along.