Carnegie are currently actively seeking a new head coach after Neil Back stepped down in the aftermath of the club's bottom-placed finish in the Aviva Premiership.
Former Doncaster boss Lynn Howells, current defence coach Simon Middleton and Greening were among a list of early contenders reportedly in the running.
However Greening, who has guided the Exiles to successive semi-finals in the Championship, claims he has had no contact with any other club.
In fact the former England and Wasps hooker insists that the first he had heard about reports linking him to Leeds came when contacted by skysports.com.
"I am remaining at London Welsh," said Greening, who previously played for Gloucester, Sale and Wasps. "It is always very flattering to be linked to other jobs but I am focused on the job here."
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
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Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
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The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.