With Hooper yet to play for England at any level, both Scotland and Wales investigated the possibility that the striker was eligible for their squads.
But Lennon believes the Harlow-born 24-year-old, who was on the fringes of England Under-21 squads earlier in his career, should be considered by Hodgson along with goalkeeper Fraser Forster, who was watched by England coach Ray Clemence against Benfica in the Champions League last week.
"In Hooper, we have a phenomenal player, not just his goals, but his play in general was of a very high standard," he said after the 4-1 win.
"If you look at his record, he does score a lot of goals and it is the hardest thing to do - and he scores in the big games.
"He is a good footballer, an intelligent footballer, very quick over five or 10 yards, his touch is sublime at times."
Hooper has risen from non-league football to the Champions League after beginning his career with Grays Athletic before moves to Southend United then Scunthorpe United, to whom Celtic paid £2.4m for his services in 2010.
"At times, he has had to play a little bit differently, particularly in Europe, but all those aspects are building up to him being the all-round striker that he is," said Lennon.
"He thrives on goals, obviously, but his link-up play is fantastic and he is developing very well."
Yet Lennon admits he will have a "selection headache" ahead of the reigning champions' trip to face Scottish Premier League leaders Motherwell on Saturday and their Champions League meeting with Spartak Moscow next midweek.
Summer signings Lassad Nouioui, the former Deportivo La Coruna striker, and fellow striker Miku, on loan from Getafe, missed Rovers' visit through injury, but they and Georgios Samaras, who was injured on international duty with Greece, are nearing fitness.
Meanwhile, midfielders Beram Kayal and Joe Ledley, neither of whom had played since August, made their return to action following injury against the Kirkcaldy side.
"It was always the plan to give Beram an hour and give Joe half an hour, so thankfully they came through that unscathed and will be fit for the weekend," added Lennon.
"Lassad and Miku will be fit as well and Georgios isn't far away either, so we are almost at a full quota coming in to a big stretch of games."
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