During a two-legged Champions League qualifier between the Swiss side and Maccabi Tel Aviv last August, Salah refused to shake hands - instead changing his boots in one instance and bumping fists with his opponents in the other - while there were also comments attributed to him expressing an anti-Israeli sentiment.
Salah insisted the comments were fictitious and his actions were a result of external pressures.
Yet Mourinho has promised to nurture the 21-year-old once his move is complete to a club owned by Russian billionaire Roman Abramovich, who is Jewish.
"It's not a concern, because we know the club Chelsea is, I know the manager I am," Mourinho said.
"I know that Chelsea's capable of helping people and making people feel the way we think people should feel, which in football and in life is to be open and respectful to every ethnicity, to every religion.
"People have the right to be what they are. Chelsea as a club and me as a manager we will be more than ready to help him."
The incident with Maccabi Tel Aviv took place under UEFA jurisdiction, but Press Association Sport understands anti-discrimination groups will be monitoring the situation.
Source : PA