The Ireland wing was one of the stars of the 2009 tour of South Africa, in which he scored four tries.
But having missed the RBS 6 Nations due to a knee injury and just returned to action, Bowe faces a race against time to secure his place on the trip to Australia.
"I would love, love to think that I could be going over there," said Bowe.
"It would be a dream come true. I absolutely adored the last Lions tour. For me, it's very much out of my hands.
"Not being involved in the Six Nations and not making it through to the semi-final in a couple of weeks of the Heineken is something that is not going to help my chances.
"I need to try and stay positive and keep playing my own game and try to get back to my own game."
Bowe makes his first start since December when he turns out against Newport Gwent Dragons.
He admits his injury-ravaged season has been frustrating but he is thrilled to be back on the pitch and is determined to do all he can to convince Warren Gatland.
"It's very difficult being injured, having to watch the six nations, watch some crucial Ulster matches, added Bowe.
"Not to be involved there and not to be playing is very frustrating and disappointing, but you have to try and take the positive out of it.
"It is a very difficult time and it does take the confidence out of you but when you get the opportunity to get back fit and back playing again, it gives you a massive lift that you are back in the fold.
"It's great to be out of the gym, out of doing your rehab and back playing the sport you love.
"The Lions is a tour of a lifetime. To go on a Lions tour is very special experience. It tests you physically, tests you mentally, tests you rugby skill but it is something I really enjoyed and got really into, so it would be great, it would be great to go on another one.
"The games come thick and fast. There is normally a big enough squad so that you may only play once, sometimes you can play twice in a week, which is pretty demanding, but the end goal is to try and get yourself picked for the test team. You pretty much do anything to try and improve your chances of that.
"I've got a couple more games before the squad is announced and who knows what could happen. At the moment for me I am very much looking at myself personally, I just have to try and get my game-time up, show that I am 100% fit and try and play some good rugby."