With the 2019 World Cup final victory over France, she became the first coach to lead two different countries to the World Cup final.
On Thursday, when the United States was eliminated from the World Cup in the round of 16, manager Vlatko Andonovski resigned. Wiegman has been mentioned as a possible replacement.
"We've seen lots of rumours, and she is a special talent - we know that. From our side, she's contracted through until 2025," said Mark Bullingham, FA Chief.
"She's doing a great job. We're obviously huge supporters of her and hopefully she feels the same way. She's someone we'd like to have with us for a very long time."
Asked whether there had been discussions with Wiegman over a new contract, Bullingham said: "We've always said we'd get to it after a tournament. We had good conversations after the Euros."
"There will be an appropriate time to do it. We've got a bit of time. She'll want to have a decent holiday after this."
FA women's technical director Kay Cossington said Wiegman and assistant coach Arjan Veurink have had "a fantastic impact" and have "embraced the England DNA across all of our teams".
Since England's European victory, the FA and Brent Council have considered plans to erect a statue honouring Wiegman in front of Wembley Stadium.
"We've made progress on that and it would be right to have something to commemorate that success outside Wembley. It's more the whole team," said Bullingham.
"You have to go through various permissions - we've gone through that. The next stage is working on the design."
When asked if Wiegman could replace men's manager Gareth Southgate, Bullingham said, "she could do anything she wants in football."
"Firstly, I think it's a bit disrespectful to the Lionesses to project it as a step up," said Bullingham.
"People always say it is 'the best man for the job'. Why does it have to be a man? Our answer is always 'it's the best person for the job'."
Despite her recent success, concerns have also been raised as to why Wiegman's salary is not equal to that of men's coach Gareth Southgate.
"I understand the question. If you look at the disparity in the market and the income coming in, that's why you've got a difference," said Bullingham.
"We don't talk about people's remuneration but I would say that Sarina is, within the market she operates, well paid. If you look at the comparison in the men's game, it's a different market."
"I really want those markets to merge over time but we're not there yet. That is the long-term objective and where we have got to get."
The Lionesses will depart Australia on Monday, and if they beat Spain, there may be a celebration in London on Tuesday or Wednesday.
