不久的將來

More formal ways:
In the near future - Cure of cancer will not be available in the near future.
In the foreseeable future - Cell phone technology will dominate human life in the foreseeable future.

Note that it's usually used with article the, because that short period of future is often defined.

Another more dramatic way of saying it is: in the immediate future.

Less formal way:
Soon - Go back to your seat, the teacher will come soon!

Just add one more

Not so distance future

the soonest future !

Answer:

in the coming future.

Example:

Hongkongers are looking forward (期待) to seeing the universal suffrage (公民普選權) to be introduced (賦予) in the coming future.

Remarks (備註) 1:

After " look forward ", it is a must to use " to " & Gerund (動名詞) ie. +ing.

Remarks (備註) 2:

Agreed with the upstair reply. " in the near future " can be your other option (選擇).

不久的將來
The near future