India's tour, scheduled for June and July, was postponed because of the coronavirus pandemic, while South Africa are due to travel in September.

"We're optimistic of holding at least one series," Connor told BBC Sport.

"It could be that we play the two series concurrently and look at a tri-series. Everything is possible."

England's men began training this week and the women are planning a return on about 22 June.

A revamped men's schedule, involving games behind closed doors, is due to be released by the end of May, with Connor explaining that women's fixtures have been involved in the discussions around holding fixtures in a 'bio-secure' environment.

"We need to get a lot of men's Test cricket played. We are completely integrated in those conversations around medical provisions, logistics, how venues and hotels would work, what the procedures would be," said the former England captain.

"We're keeping all scenarios open. It could be India first, followed by South Africa. It could be both at the same time. One thing we don't know for definite is if those teams want to come and will feel safe in coming."

'Staggering and humbling' response to coronavirus

Connor was speaking as part of the launch of the England and Wales Cricket Board's (ECB) 'Together Through This Test' campaign, which celebrates the work of more than 200 initiatives at all levels of the game in response to the coronavirus crisis.

The ECB has also established a resource hub on its website, focusing on providing physical and mental health support to the public, delivering resources to children and supporting the recreational game.

"I hope this shows the game in its best possible light," said Connor.

"It's been remarkable to see the number of initiatives going on, ranging from taking food to vulnerable people, helping the home-schooling of children, and things to lift morale. It's been staggering and humbling.

"We recognise we are in this for the long haul, and the game wants to support its participants and members."

Kent is one of the 18 first-class teams to have offered its ground to the NHS, while the county's players, staff and coaches joined with local clubs for the 'Rainbow Run' to raise funds for coronavirus appeals.

"The game has come together," said Kent chief executive Simon Storey. "We are all conscious of the responsibility we carry as Britain's summer sport."

All cricket in the UK is suspended until at least 1 July, with international fixtures set to be held first when the game does resume.

The ECB has said it is hopeful of staging domestic first-class and limited-overs cricket later in the summer.