Lennon has been struggling to secure regular first-team action at Goodison Park this term and the arrival of the former PSV star could further hurt his chances.
Nevertheless, the winger is not worried about rumours regarding Depay as he feels competition for places is only natural.
"That does not affect me and never has," Lennon told Sky Sports.
"Speculation has never bothered me and them signing Yannick Bolasie did not faze me. There is competition in all the top clubs and Everton are a massive club now.
"I have been at Spurs in the past and am used to two or three wingers or maybe four in each club. You have got to fight for your position and I am confident in my ability.
"You bide your time and if you get your chance you have got to take it."