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The phrase "appear to be heading" is correct and usable in written English.
It can be used when discussing someone's or something's perceived direction or trend, often in a speculative context.
Example: "The latest reports suggest that the economy may appear to be heading towards a recession."
Alternatives: "seem to be moving" or "look to be progressing".
Exact(37)
Instead, many of them appear to be heading for Burundi.
"You don't appear to be heading anywhere," she answered.
We appear to be heading in that direction, which is all to the good.
In some Canadian cities, particularly Toronto and Vancouver, prices appear to be heading toward record levels.
Their rage vented, the Lou Nuer fighters now appear to be heading home.
The cowboys of parliament and the press appear to be heading for an everlasting shoot-out.
Similar(23)
But they appear to be headed for a split.
But things appear to be headed back in the other direction.
A number of big countries appear to be headed for ten per cent.
American officers say both divisions appear to be headed for significant concentrations of Iraqi soldiers soon.
Congress and the White House appear to be headed for a constitutional showdown.
More suggestions(16)
appear to be participating
appear to be advancing
appear to be addressing
appear to be candidates
appear to be headlines
appear to be matters
appear to be play
appears to be heading
look to be heading
appear to be joking
appear to be paying
appear to be doing
appear to be going
appear to be melting
appear to be flying
appear to be making
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com