The off-spinner, whose presence was missed as England drew 0-0 against New Zealand in the recently-completed Test series, went under the knife in Minnesota earlier this month in an attempt to cure the long-standing problem.
As he reported for duty at Nottinghamshire's pre-season media day, Swann said: "I feel great. I want to be back as soon as possible because I'm bored stupid already. I think it would kill me if I sit down and watch too much cricket at the start of the summer without being an active part of it. I want to play as much as I can."
He added: "By the end of April I hope to be bowling. I don't know if that's realistic or not, but that's how my mind works.
"The surgeon (Dr Shawn O'Driscoll) has reassured me it was a lot more straightforward this time.
"In an ideal world I'd be fit and proving to the coach and captain that I'm bowling well to make the first Test of the summer (against New Zealand, starts May 16).
"That's my aim. Whether it's pie in the sky or too optimistic, that's the goal."
England have long been concerned about Swann's elbow, part of the reason he has been one of the most frequent beneficiaries of their rotation policy, particularly in one-day cricket.
The player himself, now 34, has previously cast doubt on his likely longevity at the top level but he was upbeat when asked about the future.
"I'm not too worried. The hunger is still strong," he said. "I love Test cricket and I'll play as long as my body can stand it, whether that's 12 Tests of 112.
"But I've not been worried about anything long term because I know I'll be fine. The last time the operation I had was far more serious and the recovery was great - he was able to sort me out and get me fit for four years of unbelievable Test cricket.
"I was bowling for three-and-a-half years relatively pain-free and that was one of the signs in New Zealand; all of a sudden I got a sore back, shoulder, abdominals.
"It was all down to the fact the elbow wasn't working properly. Now it's all clear and it should be right as rain."
- Sports & Recreation
- New Zealand