European Tour chief executive Keith Pelley says he is "hopeful" of staging the Irish Open in May.
The Made in Denmark and GolfSixes Cascais tournaments became the latest golf competitions to fall victim to the coronavirus pandemic on Thursday.
However, the tour is targeting a return at Mount Juliet on 28 May.
"We will continue to monitor this global situation in relation to coronavirus and evaluate its impact on all our tournaments," said Pelley.
"Discussions regarding the possible rescheduling of all postponed tournaments are ongoing and we remain hopeful of European Tour action resuming in Ireland at the end of May."
The European Tour has been forced into shut-down following the outbreak of Covid-19, with tournaments in Kenya, India, Malaysia, China and Spain also having been called off in recent weeks.
Made in Denmark was due to take place between 21-24 May, a week prior to the Irish Open.
World number one Rory McIlroy, 2019 Open winner Shane Lowry and defending champion Jon Rahm are among those confirmed as part of the star-studded field at Mount Juliet.
R&A evaluating Open plans
Meanwhile, the R&A have said they are undertaking a "comprehensive evaluation" of their plans with regards to The Open and Women's British Open.
The Open is due to take place at Royal St George's between 16-19 July, with the Women's British Open scheduled for 20-23 August at Royal Troon.
"Our absolute priority is to ensure the safety of players, fans, officials, staff and all involved in our championships and that will be at the forefront of our thinking as we monitor developments," said R&A chief executive Martin Slumbers.
"We have some time before we start building the infrastructure at both venues and so we are keeping the scheduled dates in place for The Open and AIG Women's British Open at this point.
"We recognise that this is a rapidly changing situation and we will keep everyone informed of any changes to our plans.
"These are difficult times but we are bearing in mind our responsibility for what's right for golf and most importantly for society."