Dempo said that the talks with Khan, who co-owns IPL-winning side Kolkata Knight Riders, were "progressing very well".
"We are discussing with Mr Shah Rukh Khan on his possible investment in the club and the only thing I can say is that talks are progressing very well," Dempo said.
"His response has been very positive. Mr Khan is very passionate about football and, apart from just involving himself in Dempo, he wants to do something for Indian football. He said that football was his first love even before cricket," Dempo added.
Dempo would not elaborate much on the details but sources said that Khan has been in talks with the Goa-based I-League champion club for a while. They said Khan has met Dempo quite a few times and he was interested in acquiring 50 per cent stake in the club.
"Talks are on and he has also met the Dempo management, including the owner, a couple of times, but it is yet to be confirmed. Some things need to be worked out before finalising the deal," a source said.
It has been learnt that the club was keen on using Khan's name and popularity in promoting the I-League champion side who have been dominating Indian football for quite a while now.
The club recently bought a 34 per cent stake in leading Danish soccer club and academy FC Midtjylland, for 12 million euros.
Dempo have won the I-league three times since its inception in 2007-08, including the inaugural edition, besides winning the erstwhile National Football League (NFL) twice.
They are also the only Indian club to make it to the semifinals of the AFC Cup, Asia's second tier club competition, in 2008.