The centre back was withdrawn in the first half of the Black Cats’ Wembley win with a calf issue, in what was his second outing since returning from a prior injury.
And Flanagan will now face another spell out of team leaving Lee Johnson without four senior central defenders – with Bailey Wright, Jordan Willis and Arbenit Xhemajli also sidelined.
But better news has come in the shape of Denver Hume, who has returned to full training this week.
Johnson has, however, previously said that the full-back will require minutes before his first-team return and a bounce game could be arranged next week to step-up his recovery.
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Ross Stewart is also back training and, having been an unused substitute in the Papa John’s Trophy Final, is now ready to make his Sunderland debut.
“Denver has now trained without restriction,” said Johnson speaking to SAFC.com
“The next step for him is to try to look at a consistent training period and minutes, so we might try to arrange a game next week behind closed doors at home against a local team.”
“Tom Flanagan is out with a hamstring injury and best case he’s going to be out for three to four weeks, which is disappointing,” he continued.
“Ross has had an amazing month, he’s has nought appearances, nought goals, nought assists and won one trophy, but on a serious note, it’s brilliant to have him back.
“We want all the players to be as fit as they can possibly be because it’s not easy and it’s unprecedented times, so soon as we get one back, we feel very grateful and very happy that we have different options.
“That’s the beauty of all our players, they all have their unique individual quality and what we’ve had to do is be very flexible to maximise that, but the more options we have the better.”
Jordan Jones and Aiden O’Brien will continue to be monitored after they picked-up injuries that ruled them out of the trip to Wembley on Sunday.