Source: Heidi and Seal Have Not Split – Yet

By Kristen Mascia

01/21/2012 at 01:25 PM EST

Seal and Heidi Klum are not headed for divorce court just yet, a source close to them tells PEOPLE.

Contrary to reports that surfaced Saturday, "They've been fighting a lot lately, but they have no plans to announce a split right now," the source says. "They're not divorcing."

But they have been weathering a rough patch.

According to the insider, in recent months, distance has tested the famously lovey-dovey pair.

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On tour to promote his new album, Soul 2, Seal recently flew solo to New York to appear on Late Show with David Letterman, then to London for more commitments.

Back together at their Brentwood, Calif., home on Saturday, "they seem to be doing a lot better," the source adds. "They're both wearing their wedding bands."

But there's more time apart on the horizon.

While Seal is due to appear this week on The Ellen DeGeneres Show, Jimmy Kimmel Live! and Tavis Smiley – all of which tape in and around Los Angeles – Klum is expected to travel to Germany soon to work on the seventh season of Germany's Next Top Model, which premieres Feb. 23.

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• With reporting by KEVIN O'DONNELL and PERNILLA CEDENHEIM