Germany attacker Werner is under contract at Leipzig until 2023, but has a release clause worth in the region of €55 million which allows him to leave the Bundesliga side this summer.
Last month the 24-year-old dropped strong hints that he could leave for Liverpool as it would "be a good fit."
However, with the impact of the coronavirus crisis on football and transfers yet unknown, RB Leipzig sporting director Krosche told Sport1 that he believes the Germany international could stay at the club.
Sport 1 claimed that Liverpool, Manchester United and Manchester City were all prepared to trigger Werner's release clause, but Krosche now believes that "everything is possible."
"We can't say how the transfer market will develop. We are starring into a very foggy crystal ball. We don't know how our resources will be and what options other clubs might have," Krosche said.
Last week, German football league (DFL) CEO Christian Seifert warned that several Bundesliga clubs might no longer exist after the pandemic subsided. Seifert called the current situation "existence-threatening" for at least half of the 36 clubs making up the upper two tiers.
However, Krosche said he believes financial constraints will not only be of concern to German clubs.
"England has similar problems like us. To bank on clocks running differently there just because they have investors is wrong," he said.
"Investors also have economic constraints. The crisis does not only hit our branch but has a worldwide impact. Today, we are not able to gauge if the current numbers [transfer fees] are sustainable in six months from now."