"within their sight" is a correct and usable phrase in written English.
You can use it when referring to something that is visible or easily accessible to another person or group of people. For example: We wanted to ensure that the children were safe, so we stayed within their sight.
4.38pm: The Murrays have this within their sights now.
Deraa, the southern city where Syria's uprising first began, is now within their sights.
With sales steadily increasing, Americans and Europeans have already taken Hello Kitty into their homes, pencilcases, wardrobes etc, and Hatoyama says world domination is within their sights.
Town after town has fallen, and now the mutineers almost have the gates of the provincial capital, Goma, within their sights, just as Nkunda did in 2008.
Thompson said they had kept the group ahead of them within their sights the whole time, as is consistent with golf etiquette.
Trump and his adopted party have (expensive) tax cuts for the rich within their sights while a plethora of progressive initiatives that predominantly affect the very poorest are now in the firing line.
Yet the prosecutors have clearly adopted a strategy of calling attention to collectors, especially well-heeled Americans, with the implicit message that every player in the global antiquities trade is within their sights.
Northern Ireland, who have already returned from Copenhagen with a valuable point, had wanted Uefa to order a replay, no doubt in the hope that it would end in a draw, a result that would not only keep Sweden within their sights but also increase the likelihood of the Danes having something to play for when Spain travel to the Parken Stadium in October.
As companies like these grow, you can imagine that concepts like Sapho's could well be within their sights, too.
If they can eradicate defensive frailties, a top-half finish should be more than within their sights".
