Eid said they would hold discussions after his return from Australia, where Bahrain have lost their first two games and play a dead rubber against Qatar on Monday in their final game.
The 35-year-old Bahraini has only been in charge since November, when he succeeded Iraq's Adnan Hamad who was dismissed during the Gulf Cup -- just three months after being appointed.
"I haven't discussed this with the board of directors or the president because we're still in the tournament, we have one match left," Eid said on Sunday about his future in the role.
"When we're back in Bahrain we can discuss these things, about whether I'll continue or not. It will be become clear after this tournament, not now."
Signup to our newsletter and follow us on Facebook and Twitter!
Bahrain's coaching merry-go-round has been spinning rapidly since Anthony Hudson took over from Argentine Gabriel Calderon in August 2013.
The Englishman was replaced by Hamad when he left to take charge of New Zealand, but the Iraqi was then rapidly dismissed during Bahrain's winless Gulf Cup.
Bahrain's track record with coaches is similar to that of 2022 World Cup hosts and fellow Gulf state Qatar, who have been through 30 since 1990.
In Australia, Bahrain were beaten 2-0 by three-time winners Iran before going down 2-1 to UAE, when they conceded the tournament's fastest record goal after just 14 seconds.
"That was a mistake, we should have put the ball out," Eid said of that goal. "My players will learn from that if they face the same situation in the next match."