The phrase "making their approach" is grammatically correct and can be used in written English.
It refers to the act of someone or something moving closer to a destination or goal. Example: "The birds flew in perfect formation, making their approach to the warm, sandy beach."
The quiet is broken, too, by planes making their approach to Manchester.
Frank Morgan Jr., commander of the Fifth Precinct of the Suffolk police, who was at the crash scene, said last night that Mr. Hughes and Mr. Carrol had radioed the airport control tower to report "dual-engine failure" while making their approach.
Tinbergen's Four Questions (Plus One), however, makes this approach intuitive and accessible to students from diverse backgrounds, making their approach to science flexible and increasing their potential for innovative thinking.
Criminals may trawl social media for personal details so they can make their approach more direct and credible.
After a while, Bobby began to hear the Dopplered gulling of the sirens as the fire trucks made their approach.
Like the rest of the choices that Abraham and Scully (who also did the lighting) made, their approach to the footage was judicious.
Or, indeed, that when he was at Wigan he had a year of his contract left when Everton made their approach.
Once again, there were disgraceful scenes at the 17th green, which ensured that Colin Montgomerie and his partner would have to wait to make their approach shot.
Journalists desiring a chat with a V.I.P. had to make their approach through a representative of Mr. Davis's label, J Records.
Jumpers make their approach down the runway at nearly top speed, plant a foot on the takeoff board, and leap into the air.
Bowyer duly made it three from three, seeing off Bristol City 2-0 in the FA Cup, but on Wednesday evening Rovers made their approach for Appleton public with Singh seemingly marginalised and managing director Derek Shaw driving the recruitment process.
