Eddie Jones remains in contention to take charge of the 2021 British & Irish Lions tour of South Africa despite his two-year contract extension to stay on as England’s head coach until August that year, the Rugby Football Union has confirmed.

The RFU has moved to secure Jones, who had planned to step down after the 2019 World Cup, for a further two years following 22 wins from 23 Tests in charge. Jones has a break clause in his contract extension, dependent on England’s World Cup performance in Japan, but assuming he stays until 2021 he will become England’s longest-serving head coach since Sir Clive Woodward.

In 2016 the RFU’s position was that Jones was “completely unavailable” for the Lions tour of New Zealand last summer but the chief executive, Steve Brown, revealed a change in the governing body’s stance. If Jones does replace Warren Gatland he would most likely need to take a sabbatical, as the New Zealander has done for the previous two tours.

“No, it [the contract extension] wouldn’t prohibit him at all,” Brown said. “Our view is that if we’re planning for success, and we’ve come out of a very successful World Cup, and Eddie is the right coach for the Lions, the arrangement isn’t going to preclude that.”

The RFU intends to appoint a long‑term successor at some point during the 2019‑20 season and according to Brown they could be working alongside Jones for “almost two years”. If the appointment requires a buy-out fee – Jones cost the £350,000 in late 2015 – and the RFU is paying two bumper salaries for upwards of 18 months, the additional cost is likely to run beyond £1m.

Brown revealed the RFU remains open to internal or external, established or developing coaches but Jones, who will play a part in the recruitment of his successor, said: “As long as I’m head coach I have the ultimate say. That’s quite simple.”

Brown refused to expand on what kind of outcome at the 2019 World Cup may result in Jones leaving the role but it would seem the semi-finals is minimum for the team ranked No 2 in the world. The break clause can also be considered an insurance policy after Stuart Lancaster’s contract was extended until 2020 less than a year before England’s flop at the 2015 World Cup, for which he was sacked. Jones said: “If we don’t win the World Cup I’ll be disappointed.”

Jones names his Six Nations squad on Thursday but his back-row options took another hit on Wednesday when James Haskell was suspended for the first two matches – in Italy on 4 February and at home against Wales six days later. Haskell, who was sent off for a dangerous tackle on Jamie Roberts last week, joins the injured trio of back-rowers – Billy Vunipola, Nathan Hughes and Tom Curry – on the sidelines.

Jones takes his squad to Portugal for a training week on Sunday and also has problems with his back three. Mike Brown cannot take part in contact training for two weeks after he was taken to hospital with blurred vision after Harlequins’ win against Wasps on Saturday, and Jack Nowell is a doubt for the opener in Italy because of an ankle injury.

“For the start of the Six Nations I think [Jack] will be touch and go,” Exeter’s head coach, Rob Baxter, said. “He’s out running around on the grass but his change of direction and top end speed are a little way off yet.”

Jones is also poised to omit Manu Tuilagi to allow the Leicester centre, who has made four appearances since his latest injury lay-off, more game time for the Tigers. “I think Eddie is quite keen to see how he goes in that Premiership block of games in February and he’s quite keen for him to get some quality game minutes with us before he looks at including at him,” the Leicester head coach, Matt O’Connor, told the Telegraph.