I would want to say something like "exams are just round the corner." , is "Shiken mou chikai desu." acceptable?
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Yes, you can use it for time as well. – 永劫回帰 Nov 9 '16 at 13:45
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近いうちに is a common expression. Means something like 'soon' or 'near future' (examples) – oals Nov 9 '16 at 19:53
Chikai 近い can be used for time definitely.
試験(が)もう近いです
Shiken(ga) mou chikai desu.
This is a totally acceptable expression, preferably with the particle 'ga'.
Yes, you can use 近い
But you can also use もうすぐ to better express the nuance of "just round the corner".
もうすぐ{LLLL}試験です。
