No, domestic cats do not understand the words, “I love you” but they understand the affection delivered by the sound of your voice when saying the words. There are two reasons for this. Firstly these are the words of the English language. A Frenchman might ask whether their cat understand the words, “Je t’aime”. Or anybody in any other country might ask whether their cat understand their language and clearly domestic cats don’t and can’t. They don’t understand any human language. They are not linguistic experts. A lot of humans do not understand the language spoken in other countries either.

The more important reason why cats don’t understand the words, “I love you” is because the concept of love is a human one. Humans themselves can’t fully explain it, so how can a domestic cat understand it?!
I think it is slightly foolish to ask whether cats understand these concepts and these human words. It is better to ask whether cats understand affection and friendship as delivered in a way which they comprehend. And the answer to that question is of course they do. There’s no question of a doubt that domestic cats understand the concept of close friendship, bonding and affection as expressed through close contact, petting, rubbing, head-butting, friendly greetings, body language in general and so on. Jackson Galaxy in the video below says that cats understand the slow blink as a sign that you love them. I disagree. But what is clear is that our body language can convey to a cat our affection for them. The feline slow blink is a sign that your cat is relaxed and content and enjoying your company.
Note: videos on this site are typically made by people other than me and held on YouTube servers or the servers of other businesses (not the server storing this website). Sometimes the videos are deleted at source which stops them working on this site. If that has happened I apologise but I have no control over it.
So if we reduce the concept of human love to one of close affection for another and substitute the words “I love you” with actions which express that affection, cats understand it all. You can see this all the time in their relationships with humans, other cats and other species of animal. It seems to me that the concept of affection for another and friendship is a universal language across all species on the planet which supports all life that we know. Even genuinely solitary animals such as the domestic cat’s wild cat ancestor can learn friendship. It is a fundamental characteristic of life.
SOME PAGES ON FELINE AFFECTION: