Kent's South African director of cricket Graham Ford turned the job down on Monday but Emburey said it had not been offered to him.
In a statement on their Web site, Middlesex said: "Following Graham Ford's rejection of the offer to become India cricket coach there has been much press speculation about John Emburey's position as the other candidate for the position.
"In response to this speculation, John met with Vinny Codrington, the chief executive of Middlesex, and told him that he does not want to leave Middlesex and wishes to continue as director of cricket.
"John would like to emphasise that at no point was he offered the role as India coach and would like to thank the BCCI for the opportunity to interview for the position."
Emburey, the 54-year-old former England off-spinner, said: "I have just got my teeth into a big new challenge at Middlesex and want to stay to complete the job and extend my 36-year association with the club."
India, who tour England next month, have been without a coach since April when former Australia captain Greg Chappell resigned following the team's failure to reach the second stage of the World Cup.