A source close to the couple tells TMZ…. "It’s not true and the recent erratic and unfounded speculation on this couple is just proving that media and overzealous fans do not know what’s going on with them and shouldn’t make wild assumptions based on zero facts. Two days ago everyone had decided they were broken up, now they’re allegedly secretly engaged? It’s whiplash-inducing."

This update comes after ESPN commentator Troy Aikman doubled down on his decision to refer to the pop star as "The Missus" during "Monday Night Football" this week.

For those who missed it, the former pro quarterback made the remark as the New Orleans Saints faced off against the Kansas City Chiefs on Monday ... with the Chiefs winning a home victory at Arrowhead Stadium.

After Troy's comment went viral, the ESPN commentator suggested he didn't pull the title out of nowhere ... saying on Barstool Sports' "Pardon My Take" podcast on Wednesday that he was told the singer and the NFL player could very likely have been engaged.

Yet, it seems Troy's insider led him astray ... as we're told this claim couldn't be further from the truth.

Nonetheless, Travis and Taylor are still very much an item ... even though the Grammy winner missed a couple of the tight end's games earlier in the season.

However, she was on hand for Monday's big win ... where she showered her man with all sorts of love while celebrating with his loved one.