Last month, Former Arsenal and France forward Thierry Henry permanently deleted all his accounts in protest.
Tottenham's Davinson Sanchez was racially abused on Instagram after last weekend's draw with Newcastle, joining a long list of high-profile players to be targeted, usually by anonymous accounts.
Asked about a potential boycott at Spurs, the manager said: “The club is thinking, analysing every detail and the club of course wants to make an impact and the decision that the club will make will be a decision that we will accept and support.
“It is an internal discussion about a sad situation.”
“In relation to Davinson, there is nothing more to add about the sadness of the situation but I would just say that he found a lot of love internally because he's a lovely guy and everybody likes him and supported him and he's fine.”
Mourinho has become a social media sensation himself this season with his usually light-hearted posts on Instagram.
Asked if he would considering coming off the platform, he said the responsibility lay not with individuals but with social media giants to act.
“I didn't think about [a boycott myself],” Mourinho said.
“The ones that can make an impact on this and resolve the problem is the media giants – everything is in their hands to end this sad situation.
“Social media can be funny, can bring everyone together, can bring people from different continents to look like they are living in the same street. I have some fun, I try to be positive and that is the way it should be.
“Unfortunately it is not like that [for everyone] but I believe even doing different things is not going to be with individuals. It is not going to be with education because I don't believe the new generations are the problem – I believe they are much, much more in the world that we want without discrimination, without bullying.
“I think it is not even a problem of education of younger ages.
“It is for the media giants to make a decision and to make their fight. If they want to win that fight, they win it for all of us.”