Doctors would have to find cells in which phase of the cell cycle to make a proper karyotype-interphase or mitosis

A karyotype involves the arrangement of a complete set of an individuals chromosomes (see attached image)

During interphase you cannot see the chromosome because they aren't condensed to the shape you can see through a microscope.

During prophase the Chromosomes become condensed and are able to be seen.

So, to answer your question, you cannot make a proper karyotype while cells are in interphase. Therefore, they would need to be in mitosis phase.

I hope this helps! I'm happy to answer any other questions you might have :)

[image sourced from: http://www.spectral-imaging.com/applications/cytogenetics/karyotyping]