Given your (subsequently added) context
Police said on Thursday they were "holding all possibilities open in respect to what might have happened" to Kamphuis and pursuing three distinct lines of inquiry: a "voluntary disappearance" including a possible suicide; an accident; or foul play.
I suggest using for foul play simply ein Verbrechen, as in this translation:
Die Polizei teilte am Donnerstag mit, sie könne noch nicht abschließend feststellen, was Kamphuis genau zugestoßen sei. Derzeit ermittle sie in drei Richtungen: "freiwilliger Abschied" einschließlich eines möglichen Suizids; ein Unfall; oder ein Verbrechen.
Rationale: In a relatively sober, factual report like this I do not see an option to use for "foul play" some of the German equivalents like "ein krummes Ding", "eine faule Sache", "eine Schweinerei" etc. as these are expression applicable only in very informal speach - i.e. speach as used in a pub perhaps, even not at the workplace.
I wonder whether the expression "foul play" in your example - the English original - is not also inappropriate in terms of style. As there is possible murder, would police officers or reporters really use "foul play" to refer to it? Or is "foul play" more appropriate for cases of deception - say, secret services or evil competitors place a corpus delicti into the house of somebody in order to smear him/her? Wouldn't that be a more typical case to be described as "foul play"? In which case a good (and high register) German equivalent would be
Hier wird mit gezinkten Karten gespielt.
Side issue (not related to the original question):
The bigger problem in that paragraph is - in my perspective - how to treat the "voluntary disappearance". Directly translated "freiwilliges Verschwinden" it sounds unprofessional and would not be part of a statement by the police. Usually they would say "freiwilliges Untertauchen", but this means that the person is still alive but does not want to be located by authorities. "Freiwilliges Untertauchen einschließlich ein möglicher Suizid" are contracting therefore and could be part of such a police statement only if written by an unexperienced junior officer (which sometimes happens, but most regularly they pass statements through a press liaison bureau that irons out stylistic mishaps). Therefore, eventually, I decided to use "freiwilliger Abschied" in this translation as this can include death. It is very unusual, though.
After reading the source in context
I later understood that this paragraph is taken from an article in the Guardian about the disappearance of a Dutch cyber security specialist. Read in context, indeed the term "foul play" seems to be meant here to suggest that some secret services or other covert, "foul" actors did something related to the dissappearance of Kamphuis, including perhaps laying false traces for investigators (e.g. a kayak and other equipment found off shore). So in this case, a translation could be:
Die Polizei teilte am Donnerstag mit, sie könne noch nicht abschließend feststellen, was Kamphuis genau zugestoßen sei. Derzeit ermittle sie in drei Richtungen: "freiwilliges Verschwinden" einschließlich eines möglichen Suizids; ein Unfall; oder es wurden absichtlich falsche Spuren gelegt.
I admit that this shifts the meaning in one specific direction, and that "foul play" is open for a broader interpretation. However, my reading of "foul play" is anyway not so much of violently causing somebody's death, rather the terms seems to be related to activities to mislead an investigation.