The move was announced yesterday as Huntsworth reported strong trading in 2019, with pre-tax profit up 27 per cent to £39.1m on revenue up 18 per cent to £264.9m.
The sale requires approval from Huntsworth shareholders at its AGM, expected in May, and from various national competition authorities.
"There's no guaranteed timetable," said Taaffe. "The earliest would be quarter three, and the longest would be five months."
Asked if he's confident the deal will complete, the chief executive said: "It's being regarded within the City as a fair offer. That usually is a basis for some confidence but anything could happen, nobody knows."
CD&R, which is based in the US and London, has invested in a number of healthcare businesses.
Huntsworth has been growing its healthcare marcomms business in recent years – healthcare made up 72 per cent of revenue in 2019, up from 67 per cent in 2018.
That followed the acquisition of healthcare agencies Kyne and Creativ-Ceutical alongside like-for-like revenue growth in healthcare of five per cent.
Taaffe said: "They [CD&R] like Huntsworth as a platform in what they call pharma services. They are excited by the opportunities in it, they are excited by what we've done in the last four years since we've been moving this group around.
"We've grown the business by about 35 per cent CAGR (compound annual growth rate) and 27 per cent EPS (earnings per share) over the period, which is obviously very strong and they like that growth story.
"Private equity tends to like strong, growing companies and we're a strong, growing company."
At its full-year results, Huntsworth chairman David Lowden said "standout performances" in PR were in Citigate Dewe Rogerson in Asia and Grayling in the UK and Brussels, all of which achieved double-digit revenue growth.
Asked if issues around the unstable political situation in the UK affected trading in 2019, Taaffe said: "They just didn't. Grayling, which has a deep public affairs capability in the UK and across Europe, benefited from that political instability, and the growing scrutiny of businesses helped CDR in the UK as well. They're involved in a number of transactions and public pressure-type situations with their clients."
Taaffe described trading at Red as "solid" and Quiller had "a great year as well". The company did not provide trading figures for the individual agencies.
"The UK market for us in 2019 was a very strong year," he said. "While we don't know where the coronavirus will lead us in 2020, we're currently looking at another strong year."
Taaffe had earlier described trading in Europe in 2018 as "sluggish", but pointed to an improved picture in 2019 for the PR division: "In 2019 Continental Europe for Grayling and also for Citigate in France did very well. They returned to growth and they retained a profit improvement.
"In the case of Grayling, both the UK and Continental Europe grew, and in the case of Citigate it was the same."
There was also "very strong growth" at Citigate in Asia, where a Tokyo office opened in 2019, Taaffe added.