Magnussen, 20, is currently leading the Formula Renault 3.5 Series and tested for McLaren at Silverstone last week.
Magnussen also participated in last year’s young driver test for the team in Abu Dhabi.
“Yes we are looking to do just that,” Whitmarsh said when asked whether McLaren was looking into 2014 options for Magnussen.
“We had offered Kevin to Force India [for the Silverstone test], who had agreed to run him. But they changed their plans at the last minute. Given that he thought he was running for Force India we felt we should run him that day.”
With current drivers Jenson Button and Sergio Perez having contracts for next season, Whitmarsh stressed that Magnussen would not be thrown in at the deep end.
“There is a tremendous amount of expectation and pressure on being a McLaren driver. I know we have had exceptions, but generally we don’t have rookies in the car and we have to try to develop drivers for the longer term,” he said.
“F1 has not been good at developing drivers. At the moment we have some really interesting programmes, but they are a few years away from having a particular impact on this team.”
McLaren’s current partnership with Force India expires at the end of this season, meaning that Magnussen’s best hope could be with Marussia.
However, Marussia’s financial situation – which would probably require them to seek a driver with a healthy sponsorship package – combined with their Ferrari engine deal, which seemingly ties Jules Bianchi to the team, could limit Magnussen’s opportunities.