After Barca beat Celtic 1-0 in Tuesday's Champions League meeting in Glasgow, impressed visiting defender Dani Alves claimed Forster would be the perfect choice to replace Victor Valdes when he quits the Catalan club next year.
Alves had just watched Forster make three terrific saves in the closing stages of the game to keep the visitors at bay and the big Geordie, who was linked with Portuguese club Benfica over the summer, was subsequently then called up to Roy Hodgson's England squad for World Cup qualifiers against Montenegro and Poland.
Ahead of the Scottish Premiership clash with Motherwell at Parkhead on Saturday, Celtic boss Lennon embraced Forster's increasing profile and reputation.
"I don't want to stop the speculation," he said. "I want him to keep playing well and if an opportunity like that arises then who am I to stand in his way?
"Opportunities like that come once in a lifetime.
"It is just fantastic that people are talking about him in this fashion although I hope it is not short-termism.
"I want it to be for the long term. Short term, he is here with us and thriving."
Hodgson revealed he will stick by Hart despite a dodgy performance in Manchester City's 3-1 Champions League defeat to Bayern Munich on Wednesday night.
Lennon believes Forster would be "unquestionably" ready if called upon to make his England debut but understands Hodgson's desire to stick with his current number one.
"Fraser has been playing brilliantly in huge games for the last two and half years," he said.
"It is a shame that it has to take Champions League performances for everyone to sit up and take notice.
"His character and temperament is excellent and he has the talent.
"He makes saves that not many keepers can make and he has improved every year since he came here.
"It is brilliant for him, great recognition and testament to his talent that he is playing his club football in Scotland and he is knocking on the door for the England number one spot.
"I understand Roy's view. Joe is his number one and there are two crucial qualifiers coming up.
"Fraser has to stay in the place he is in and keep pushing.
"But has Joe played badly for England? He maybe had a bad night in midweek but Joe is a world class goalkeeper. What he has now is stiff competition.
"While I am waxing lyrical about Fraser, there are days he can't keep the ball out of the net and they all have bad days."
Lennon stood by his claim skipper Scott Brown should not have been dismissed against Barca for flicking out at Neymar after an initial foul on the Brazilian star.
The Hoops boss said: "He is disappointed, more disappointed in the context that we were down to 10 men against a great side.
"But I have to say my team were brilliant, they did everything I asked apart from a two or three minute spell.
"But huge steps were taken at this level.
"The way this team and club has progressed has been phenomenal and the only disappointment for Scott is he will miss the next game (against Ajax). He has been playing so well and he will play tomorrow."
Despite taking on the might of Barcelona in front of another full-house at Celtic Park, Lennon does not believe that his players will need motivated for the visit of the Steelmen.
"When you have been competing against the best teams and challenging them, it gives you a great lift," he said.
"The players came in today and the quality of training was exceptional.
"They have had a look at what the top level of football really is and they are not far away and they will get a huge lift out of that so in terms of motivating the for tomorrow's game, I don't think they will have much of a problem."
Lennon revealed that Celtic will be speaking to Georgios Samaras about a new deal while the club are also revisiting contract talks with Anthony Stokes.
The former Celtic skipper said: "We are aware that he (Samaras) is out of contract at the end of the season.
"We will be speaking to Georgios and his representatives pretty soon and we will speak to Stokesy again. I don't know when but it will happen."