City sources said a majority of shareholders are set to back Quarta at WPP's annual general meeting on 13 June, although he is still likely to face some opposition over the way he handled the departure of Sorrell as chief executive in April.
There could be greater opposition against the remuneration report because of the way WPP treated Sorrell as a "good leaver", which means he is able to collect long-term share awards worth about £20m as a pay-off.
It is thought a significant minority of shareholders could vote against the remuneration report in the non-binding vote.
Some investors have criticised WPP for refusing to reveal details of its investigation into allegations of personal misconduct that led to Sorrell’s resignation.
WPP had said it was a "private" matter.
It subsequently emerged that Sorrell had no non-compete clause and he has already set up a new data, technology and content company, S4 Capital – a move that has further angered some WPP shareholders.
A majority of investors are expected to approve the re-election of all the directors and the remuneration report at the AGM because ISS, an influential shareholder advisory group, has given its support.
Glass Lewis, another advisory group, has recommended a vote against Quarta.
The remuneration report shows Sorrell received no short-term bonus in 2017 but still collected £14m, including a £10m long-term share award.
A WPP spokesman declined to comment.
It is understood that Sorrell, who continues to hold nearly 2% of WPP, has no plan to attend the AGM in London.
Quarta has used interviews with The Wall Street Journal and the Financial Times ahead of the meeting to send a conciliatory message to shareholders.
He said the search for a replacement for a new chief executive is advancing, with about 12 candidates under consideration, and he warned Sorrell of "consequences" if the former chief executive divulged any confidential information about WPP in the building of his new company.
Quarta added that the company has "no sacred cows" and would consider selling and merging subsidiaries.
WPP’s share price fell a third during Sorrell’s last year in charge as he tried to simplify the group.
The former chief executive liked to talk about "horizontality", his strategy for getting WPP agencies to work together for the same client, but Quarta said the group was ditching the concept after senior executives said it was not working.
"You won’t hear that word being used any more," Quarta said.
Sorrell has denied the allegations about his personal conduct "unreservedly".
The former WPP boss has raised £51m to launch S4 Capital and will have a 75% stake.
Investors have said they could invest a further £150m.
There has been speculation that Sorrell could be interested in bidding for WPP’s data arm, Kantar, which has been valued at upwards of £3bn.
However, an observer suggested it is unlikely that Sorrell would want to mount such a bid because S4 Capital would need to team up with another buyer and could end up with only a small stake and little control.