Morgan suffered a back spasm during England's match against the West Indies during their triumphant World Cup campaign and had to leave the field in Southampton. His training throughout the tournament was limited after that.
Morgan was at Lord's on Friday and was commemorated during the Lunch break of the second Ashes Test by England and Wales Cricket Board chairman Colin Graves.
"I need more time to think, that's the honest answer," Morgan told Test Match Special when asked if he would lead England into the T20 World Cup in 2021. "It's a big decision, a big commitment. Given the injury that I went through in the World Cup, I need time to get fully fit.
"I actually need the season to end pretty soon so I can have that time to physically get fit and guarantee that it's not an injury risk between this year and next, and then I'll be able to make a call on that."
Morgan has been playing for Middlesex in the T20 Blast after a two-week break following the World Cup. He admitted that while he "absolutely" wants to lead the team next year, he felt "physically and mentally cooked" after the World Cup.
"As captain, you take a little bit more on board than probably just being a player," he said.
( With inputs from IANS )
