The St Mirren star was sensational in Sunday's Scottish Communities League Cup final victory over Hearts. But with Mac out of contract in the summer, the manager has made the 25-year-old top of his to-do list.
McGowan exclusively revealed to SportTimes yesterday that the cup success was swaying him in the direction of a new Paisley deal.
Lennon said: "We have a few lads who are going out of contract in the summer and Paul is one of those and very much a priority.
"We have started talks with his representatives and these will be ongoing. We want him to stay at St Mirren and continue to grow as a player with us.
"Paul showed what he is capable of at Hampden on the big stage and we believe he has better still to come. We want him to realise his potential with St Mirren."
Lennon has already re-signed talismanic striker Stevie Thompson until the summer of 2014 and burgeoning defensive talent Marc McAusland was handed a new two-year deal to extend his stay with Saints until summer 2015 last week.
But the Buddies boss has still to nail down Gary Teale, Craig Samson, Graham Carey and Sam Parkin from his cup winning side.
In the wake of his greatest managerial triumph, Lennon was keen to thank the Paisley club's board for taking a chance on him when they signed him from Cowdenbeath a couple of years back.
He said: "The St Mirren board took a chance on me when I hadn't managed above Second Division level and was untested in the top league. Hopefully the first ever League Cup trophy in our 136-year club history is pay back for that faith.
"But we are a community club and you saw that at Hampden with the way the town of Paisley turned out for us and also the way the fans filled the streets of Paisley when we paraded the trophy at night in the city.
"These were magical moments for everyone at the club and the people of Paisley and I will never forget them."