The phrase "to suspect a link" means to believe or have a feeling that there may be a connection or relationship between two things or events, even though it is not yet certain or proven. Full definition
Many researchers suspect a link between pain and lifespan. (newscientist.com)
Even if the vet does suspect a link, there is no law to make him report the suspected reaction. (siriusdog.com)
A poor night's sleep is enough to put anyone in a bad mood, and although scientists have long suspected a link between mood and sleep, the molecular basis of this connection remained a mystery. (sciencemag.org)