Spain's Campos, one of four new teams in an expanded F1 grid in the new season, have so far named only one driver, Brazilian Bruno Senna, nephew of late F1 world champion Ayrton Senna and Chandhok's former GP2 team mate.
"We are in talks with (Campos team principal) Colin (Kolles) and hope to confirm a deal very soon," the Indian driver's father and manager Vicky Chandhok said in a statement.
India's only Formula One driver to date is Narain Karthikeyan, who was with Jordan in 2005.
"We have been very impressed with Karun's performance in GP2 and are close to finalising a deal with him," Kolles said in a statement released by Vicky Chandhok.
"India is a great country and it would be great for the sport to have an Indian driver on the grid. However we will be in a better position to comment on this over the next few days.
"My aim now is to make sure that we are there on the grid in Bahrain which will be a huge achievement in itself. We are moving in the right direction and will do everything in our power to make sure we are running in Bahrain, with Karun in the car."
The Bahrain Grand Prix opens the season on March 14.
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