Morgan, England's one-day international captain, and Alex Hales, who opened in both Test and limited overs cricket this season, informed the selectors before Friday's squad announcement they would not be touring Bangladesh.
Former Ireland batsman Morgan has won plaudits for overseeing an England revival in 50-over cricket following their embarrassing first-round exit at last year's World Cup.
"Eoin has done exceptionally well as captain," national selector Whitaker told reporters at Trent Bridge after announcing the squads for the Bangladesh tour.
"It's slightly disappointing that he's turned this opportunity down, but we expect him to be captain in India."
Whitaker, a former England batsman, added: "At the same time, we'll review as we do after every series. And all I'll say is, I expect him to be captain in India."
The tour, which begins on September 30 and will include two Tests and three ODIs, had been called into question after an attack on a cafe in Dhaka in July which saw 20 hostages killed, including 18 foreigners.
Michael Vaughan, a former England captain, was scathing about Morgan's decision not to travel to Bangladesh.
"Morgan has made a huge mistake," Vaughan wrote in his Daily Telegraph column on Monday.
"You tell (your team) to be strong so they can go the extra yard.
"I do not see how he can look them in the eye and ask them to do that in the future."
But Jos Buttler, who earlier this week was appointed to lead the one-day side in Bangladesh, said he regarded himself as a stand-in skipper and that he expected Morgan to regain the captaincy for England's three ODIs and three Twenty20s in India in January and February.
"He's done a fantastic job over the last 18 months.
"He's been one of the main reasons, if not the main reason, for the turnaround in fortunes," the dynamic 26-year-old Lancashire wicket-keeper/batsman insisted.
"The style of cricket he's got the side playing is something we want to continue and keep playing that brand of cricket."
Buttler added: "He (Morgan) has made the decision that is right for him and it is not one he has taken lightly...People should respect that.
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