Strauss, 35, was set to play for county side Middlesex against Worcestershire following the Test series loss to South Africa but withdrew from the team on the morning of the match starting Tuesday.
And a couple of hours after the England one-day side suffered an 80-run thrashing by the Proteas in Southampton later Tuesday, the ECB announced that managing director Hugh Morris would be holding a press conference at Lord's at noon (1100 GMT) on Wednesday.
Meanwhile ECB chairman Giles Clarke will give a separate media briefing at Derby at 2pm (1300 GMT) on Wednesday.
That two of English cricket's most senior administrators have both decided to make previously unscheduled public statements on the same day suggests the future of both Strauss and Pietersen could be on the agenda.
Pietersen has been sidelined from England action since making 149 in the drawn second Test at Headingley after he admitted sending "provocative" texts to South African players.
Some of these were alleged to have been critical of Strauss, Pietersen's successor as England captain.
Strauss, in charge since 2009, saw England lose their number one ranked Test status to South Africa this month following a 2-0 defeat in a three-match series where the opening batsman struggled for runs.
The left-hander, asked recently if he would be in charge for the upcoming tour of India, replied: "It's probably hard to answer that after the week that's just gone by. It's been a tiring week.
"We all need to sit down -- myself and (coach) Andy Flower in particular -- and try and map out the way forward."
The ECB refused to say anything Tuesday other than issue a brief statement giving the details of Morris and Clarke's respective news conferences.
Strauss, 35, has enjoyed modest returns with the bat in recent years and his 122 against the West Indies in May was his first Test century since November 2010.
He followed up with another century, his 21st and one shy of the England all-time record, at Trent Bridge but averaged just 17.83 in six innings against the South Africans.
Were Strauss, who has led England to home and away Ashes series wins, to resign the Test captaincy he would be the third England skipper to be 'seen off' in as many tours of England by South Africa captain Graeme Smith.
Nasser Hussain resigned during the England-South Africa series in 2003, Smith's first series as Proteas skipper, with Michael Vaughan standing down five years later.
Smith, who made 52 against England in Tuesday's one-dayer, remains the Proteas' Test captain but the one-day side is now led by AB de Villiers.