Domingo has been in the role since May 2013 and his contract ends in August.
Cricket South Africa have said they are "resolved to begin a recruitment process" as they look to appoint a head coach "through to the 2019 World Cup".
South Africa will play three one-day internationals, three Twenty20 games and four Test matches against England.
Domingo's side are currently ranked third in Tests, second in one-day internationals and fourth in T20 cricket.
The 42-year-old guided his team to a 3-0 Test series win over Sri Lanka earlier this month and a 2-1 away Test series success in Australia in November.
South Africa won the first of five one-day internationals against Sri Lanka on Saturday with a convincing eight-wicket victory at Port Elizabeth.
Sri Lanka were bowled out for 181 and South Africa reached 185-2 with 15.4 overs remaining with Hashim Amla scoring 57 and Faf du Plessis making an unbeaten 55.

The body of Andraya Lyons, 39, was found in Drew Street, Swindon at 05:40 GMT on Saturday.
Anthony Porter, 32, has appeared before Swindon Magistrates' Court charged with murder.
Her family said: "We are completely devastated to have lost Andraya... The past few days have been really difficult for us as a family."
"She was a devoted mum to her boys and very much loved by all who knew her," they said.  Adding: "We will always treasure the memories we have of Andraya."
Mr Porter, also from Swindon, has been remanded in custody and will appear before Bristol Crown Court on Wednesday.

Paula Vasco-Knight, 53, broke down as she changed her plea on the second day of her trial at Exeter Crown Court.
She used £11,072 of NHS cash to pay her husband Stephen, 46, for work on an equality and diversity publication called Transform, which never existed.
Her husband also changed his plea to admit fraud.
More on the fraud case and other stories from Devon and Cornwall
Former nurse Vasco-Knight, of Runcorn, Cheshire, shook and sobbed uncontrollably as she changed her plea to one of the two charges of fraud she faced.
Recorder Don Tait adjourned sentence until March but warned the Vasco-Knights that a "custodial sentence is a distinct possibility".
He told the jury: "As far as Mrs Vasco-Knight is concerned, she has fallen a long way, hasn't she, but that is her responsibility."
Vasco-Knight was CEO at the South Devon NHS Foundation Trust and the national lead for equalities for NHS England when the offence occurred.
The newsletter was commissioned by her in April 2013 and produced by her husband's firm Thinking Caps that July, the court heard.
But it was a "sham", cut and pasted from a research paper by the Kings Fund charity, said Gareth Evans, prosecuting.
He said Vasco-Knight's failure to declare an interest in Thinking Caps was a criminal offence and a "massive breach of trust and abuse of her position as chief executive".
Vasco-Knight later tried to blame Habib Naqvi, a senior manager in the NHS, for commissioning the newsletter.
Mr Naqvi, 28, of Bristol, was cleared of two counts of aiding and abetting.
The prosecution offered no evidence on the second fraud charge against Mrs Vasco-Knight of swindling £9,000 from the NHS.
She and her husband were released on bail to 10 March for sentencing.
Sue Frith, managing director of NHS Protect, which conducted the investigation, said Vasco-Knight's meteoric career path had been "an inspiration to so many" and her fraud was a "huge disappointment and shock to many".
South Africa head coach Russell Domingo will have to reapply for his job if he wants to stay in charge of the team after their summer tour of England.
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Tributes have been paid to a "devoted mum" found dead after a house fire.
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A former NHS equality boss has been warned she could face jail for swindling £11,000 by diverting funds to her husband.