I've heard that there is a "family" of languages called the Uralic family. I looked up the association between the two languages. I found that there are possible cognates on Wikipedia.
I am floating the idea that the Uralic languages are related to the Indo-European languages like Latin, Greek, Sanskrit, etc. but I had a hard time finding anything that agrees with this. I think that they are more similar to the Germanic or Italic (especially Germanic) language families.
For example, the words no/not are the same in both languages: *ne. This shows a link, possibly through Uralic breaking off of Indo-European. The word for water, *weti sounds like the English word wet for the Germanic languages. For the Italic (Latin), the word is *mina in Uralic and in latin it is mihi.
I don't think so, but I've also heard that this topic is hotly debated, even among professional linguists.