The former Brentford boss has done a remarkable job at Ibrox, with the Glasgow giants gaining promotion to the Scottish Premiership with ease.
Rangers have also won the Scottish Challenge Cup and have progressed to the final of the Scottish Cup this season.
According to a recent report in The Scottish Sun, Everton are interested in appointing Warburton as the manager in the summer.
Former Celtic boss Lennon believes that Warburton will not leave the Gers in the summer.
The former Bolton Wanderers manager believes that Rangers’ clash with Old Firm rivals Celtic in the semi-finals of the Scottish Cup this season would have convinced the Englishman to remain at the Gers.
“I think it’s an important summer for them in terms of holding onto him,” Lennon told talkSPORT when asked about Warburton’s future at Rangers.
“I am sure there is a lot of interest in him, but I think once he got a taste of that semi-final, he probably wouldn’t get that anywhere else and he might want to have more of it because it is quite intoxicating.”
Warburton has proven himself to be a very good manager, first at Brentford and now at Rangers.
It is understandable why Merseyside outfit Everton are (reportedly) interested in the 53-year-old, but it would be a huge surprise if he stepped down from his role at the Gers in the summer.