Manchester United's interest may've come out of the blue, but at Rayo, they've always been confident of Baptistao's ability - it was just a matter of the 20 year-old getting beyond his troublesome collarbone.
The sale of Michu may've helped accelerate Baptistao's introduction this season, but he was always going to prove himself at Primera Division level, whether it was alongside the new Swansea City hero or as his replacement.
An exciting start to the season was enough for United manager Sir Alex Ferguson to post brother Martin, the club's chief scout, to check on Baptistao last month.
The ease with which he has taken to the Primera justifies Rayo's support for the 20 year-old as he struggled for form and fitness the previous season.
He explains: "I've had to deal with injuries. Last year, I did preseason with the first team, but a little before starting the season, I fractured my collarbone and was out for four months. When I came back, in the first game I fractured my collarbone again.
"Last season, I played only eight times. I scored four goals, but still was not right. I had lost a lot of confidence and I was a little overweight. So, to now be where I am this season is exceptional. The support of the staff at Rayo has been incredible."
An attacking midfielder, Baptistao developed his silky skills playing futsal in his native Brazil - with and against Santos star Neymar. The pair grew up in the same neighbourhood and are still close.
"We played together in the Santos futsal team. We played football, went to BBQs at our parents' houses ... A few months ago there was even one (BBQ) at his house and we talked, it was small talk, remembering the past. He is a very good person, humble, always remembering where he came from. I think all who know him say that. In addition, of course, he is a phenomenal player. From childhood, you could already see that he was different."
Baptistao is no mug either and his impact this season has bigger clubs across Europe now taking notice.
"I am very happy at Rayo and the fans can be calm. I do not want to leave in January. I owe everything to Rayo. My story is thanks to their support," says Baptistao.
Baptistao is on a shortlist of names at United as Ferguson considers a new attacking midfield signing. Porto winger James Rodriguez and Benfica's Nico Gaitan have both been scouted extensively in the last 12 months and now the focus has turned to the Brazilian.
Having joined Rayo as a 15 year-old, the need for a UK work permit is a non-issue for Baptistao, who actually boasts an Italian passport and won't rule out committing to Spain - just as Barcelona midfielder Thiago Alcantara and former Real Madrid striker Rodrigo Moreno both have in recent times, despite being Brazilian born.
"Today I have Italian citizenship because of my great-grandfather, although I do not do anything Italian! I am also applying for my Spanish passport (another great-grandfather of Léo's is Spanish). If an opportunity arrives to commit to the Spanish national team, why not? It is one of the best in the world.
"But of course I want to reach for the Selecao. It is the dream of all Brazilian players around the world."
Baptistao was spotted at the Vincente Calderon a fortnight ago to see Atletico Madrid defeat Real Zaragoza. His presence was played down by Rayo officials, but there is speculation that Diego Simeone wants him signed for next season.
Wherever the truth may lay, if Baptistao, at 20, has managers the calibre of Ferguson and Simeone chasing his signature, then it won't be just as a BBQ guest that Leo will be mixing with Neymar again.