Woods, McIlroy set to resume their dual at Abu Dhabi Golf Championship

FILE - In this Aug. 12, 2012 file photo, Rory McIlroy of Northern Ireland celebrates his victory on the 18th green in the final round of the PGA Championship golf tournament on the Ocean Course of the Kiawah Island Golf Resort in Kiawah Island, S.C. Nike says it has signed a sponsorship deal with No. 1-ranked McIlroy for a reported $200 million. (AP Photo/Lynne Sladky, File) (The Associated Press)

Current World Number One golf champion Rory McIlroy talks to the journalists during a press conference announcing his partnership with Nike ahead of the 2013 edition of the Abu Dhabi HSBC Golf championship in Abu Dhabi, United Arab Emirates, Monday, Jan. 14, 2013. (AP Photo/Manuel Salazar) (The Associated Press)

The world's two top golfers are meeting more and more often on the course, but neither No. 1-ranked Rory McIlroy or Tiger Woods are ready to call it a rivalry.

The pair, set to meet at this week's Abu Dhabi Golf Championship, have established a blossoming relationship since playing together for the first three rounds of last year's tournament and have expressed a mutual respect for one another's game.

But for a more heated rivalry to emerge, they both agreed they need to face each other Sunday with a tournament at stake. It has yet to happen, although Woods did make a run at McIlroy in last year's Honda Classic with a birdie-eagle finish.

Woods and McIlroy are paired together for first two rounds at Abu Dhabi starting Thursday.