Pole Kubica and Renault have reached an agreement and are only awaiting confirmation to make the deal official from the driver's current Formula One team BMW Sauber, the report said.
Kubica, 24 finished fourth in the drivers' world championship last year, securing his only grand prix win in Canada.
Renault, who need a replacement for Ferrari-bound Spaniard Alonso, were unavailable for comment.
Massa returns to Maranello
Meanwhile, Felipe Massa returned to Ferrari's headquarters at Maranello on Monday for the first time since fracturing his skull at the Hungarian Grand Prix in July.
The Brazilian, in line to race again at the start of next season if not sooner, will work on a simulator and improve his fitness in the coming days with a decision not yet taken on when he will test a 2007 car as part of his comeback.
"I'm finally back home," Massa told www.ferrari.com.
"This is my second family and I couldn't wait to see them again, all the people I've been working with for many years and who have been close to me these days. There's lots to do, but I'm happy."
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