Border said the first Test, which is scheduled to begin on December 4, should go on but it can start on December 8.
"The game must go on but I do have some misgivings about the timing of the first Test against India, starting next Thursday. With Phillip's funeral likely to be held next week, I think the Gabba Test should be pushed back three days to give players more time to grieve," Border said.
Border said that if the Gabba Test was pushed back to start next Sunday, "it would give everyone a chance to deal with things without being rushed".
"The second Test in Adelaide could then be pushed back three days, and none of this would impact on the Boxing Day or New Year's Tests," the former captain said.
More From This Section
Four Test players -- David Warner, Shane Watson, Brad Haddin and Nathan Lyon -- were on the field when Hughes was struck and they have already said that they are not in perfect state of mind to return to competitive cricket, which put the opening Test in doubt.
Border said he felt for Abbott who must be feeling terrible after the tragic incident.