Lewis, a natural forward who has been employed in more of an attacking midfield role, has started all three games for the Robins since being handed his debut against Port Vale, even scoring in Saturday's FA Cup defeat at Torquay.
But when asked about interest from the top-flight, the level-headed youngster said: "When I see it, I look at it but I don't really think about it too much because it can put you off in some ways. Obviously you see it and take it on board but then I carry on playing and doing my job for Cheltenham."
Acting Cheltenham manager John Schofield recently insisted clubs of that calibre should be looking at Lewis, such is his ability and character.
To that, he replied: "It's nice to hear your manager saying stuff about you like that and believing you're good enough to play for those teams. When the manager thinks that of you then it gives you more belief to express yourself on the pitch even more."