Reports in the Netherlands say ex-Manchester United defender Jaap Stam, who recently left his role as a coach at Ajax, is a contender for the job.
McDermott, 55, returned to the Madejski Stadium in December for his second spell as boss of the Royals.
But he only won nine of his 30 games in charge and the Berkshire side finished 17th in the second tier.
A club statement said it had been a "difficult decision" for the board of directors to relieve McDermott of his duties.
Reading said they would now undertake a "rigorous recruitment process" in order to identify the former Arsenal midfielder's successor.
McDermott led the Royals to promotion to the Premier League in 2011-12, but he left the club in March 2013 after just over three years in charge.
Reading had also enjoyed considerable cup success under McDermott, reaching the FA Cup quarter-finals in 2010 and 2011.
He agreed a two-and-a-half-year deal on his return to the club in December and again led the Royals to the last eight of the FA Cup, where they were beaten by Crystal Palace.
Reading lost six of their final seven Championship games this season and finished the campaign 12 points above the relegation zone.

Items worth more than £36 sent from the islands will incur VAT from 1 January 2013. The limit was £40.
A gift is defined as an item sent between two private people, such as a birthday or Christmas gift.
Jersey and Guernsey Post allow people to pay the VAT in advance so that the recipient is not charged by the UK Post Office.
A spokesman for Jersey Post said the recipient could have to pay the VAT and an £8 charge set by the Post Office, if the sender did not pre-pay for the item.
VAT is charged on all commercial parcels sent from Jersey to the UK after the end of Low Value Consignment Relief in April 2012. This loophole previously allowed for commercial items worth less than £15 to be sent VAT free.
HM Revenue and Customs says the change is due to a revaluation of the euro compared to the pound.
Championship side Reading have sacked manager Brian McDermott after just over five months in charge.
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The maximum value of gifts sent from the Channel Islands to the UK without incurring VAT has dropped.