Born in Denmark, Khan will join Kevin Pietersen's squad if they decide later on Sunday to return to India following last month's terrorist attacks in Mumbai. That decision will follow scrutiny of the latest security reports from the country.
Yorkshire leg-spinner Adil Rashid will also travel with the squad but has not officially been added to it.
Sidebottom is not among those currently preparing in Abu Dhabi for a series set to start in Chennai on Thursday, having suffered a side strain during the aborted one-day leg of the pre-Christmas tour.
Khan, 28, was awarded British citizenship in 2006 - following a breakthrough season for Kent a year earlier.