The Daily Mail says Chelsea are pondering a £3million bid for South Africa international Pienaar.
The 28-year-old midfielder is out of contract in the summer and looked destined to join Tottenham but Carlo Ancelotti is eager to freshen up his squad and is willing to test Everton's resistance to a sale.
The added bonus for Chelsea is that Pienaar is not cup-tied in Europe.
Everton manager David Moyes desperately needs funds to strengthen his side with a striker, but he is loath to sell the South African - especially with midfielder Tim Cahill away with Australia at the Asian Cup.
Moyes would struggle to replace Pienaar for £3m and would prefer to gamble on the free market in the summer unless Chelsea have makeweights to offer on loan.