The Daily Mail were among the media outlets talking up a transfer in late May (in Sami Mokbel's story). Last week, the same newspaper was also carrying quotes from the player he might be happy to stay at Barcelona.
Villa, however, did not rule a move out either.
"We’ll need to analyze many things during the summer and then we’ll see," he reflected. "Right now I’m not thinking about anything else than playing football."
With a Confederations Cup campaign with Spain to focus on, his club future is understandably on the back burner for now.
If Tottenham's interest in the World Cup and European Championship-winning striker is genuine, will/should they be prepared to wait on Villa?
In the meantime, Spurs will not want to lose out on other targets, not when their need for some extra quality upfront is so urgent.
The Brazilian's agent, Vinicius Prates, was quoted by SkySports.com last week as saying a move to Spurs was still a possibility.
Should manager Andre Villas-Boas believe both are additions that can improve his squad, ideally, he will be able to make room for both.
If not—and it becomes a case of choosing one or the other—Villa would be a hard choice to pass up.
There is certainly a compelling case for signing Damiao—one that Bleacher Report's Christopher Atkins outlined last month.
As Atkins concluded in his article, the possibility of Villas-Boas being able to develop him "into one of the most feared attacking players in Europe," is a tempting prospect.
But while there remains doubts about how big Damiao's potential upside is, the more likely guarantee of Villa is arguably even more tempting.
The Spain hitman is already one of his continent's most feared attackers.
After an injury-hit 2011-12, Villa returned to net 16 goals for Barcelona, this despite the Catalans' frontline becoming increasingly dominated by the superb Lionel Messi.
If Villa seeks a move, he will be keen to reassert his relevance on the European stage. That hunger, combined with the evidence of his effectiveness after returning from those earlier injuries, might be what leads Spurs to overlooking concerns over his age.
Hesitance, on Spurs' part, about investing so much on a 31-year-old may be something holding them back. The Daily Mail suggested a £10 million transfer fee, while Villa's wages will be a hefty sum too.
Age can be an overrated concern though. One need only look at the examples of Miroslav Klose (35) and Frank Lampard (34) this season to see this—both scored 15 each in the league for Lazio and Chelsea respectively.
Jurgen Klinsmann was 30 when he joined Spurs in 1994, and he went on to enjoy one of the finest campaigns of his career.
Klinsmann is somewhat of a pertinent comparison. Like the German, Villa would not have previously played in England. A move would also offer a challenging new experience for a player looking for a fresh start.
Villa is also the kind of talent that could provide an instant boost to the club, the kind of which Klinsmann provided almost 20 years ago at White Hart Lane.
It should not even be an issue that Villa might not be the long-term solution to Spurs' striking issue, one that the 23-year-old Damiao might possibly become.
Spurs need a goalscorer who can hit the ground running. Villa might need a little time to adjust to a new country, but if the experiences of compatriots like Fernando Torres and Juan Mata are anything to go by, he will not need too long.
With all due respect to Tottenham's current crop of forwards, Villa is a class above them. Even if his stay would just be for a year or two, which is better than having a younger striker whose impact is not so immediate.
Jermain Defoe and Emmanuel Adebayor may still have roles to play in Villas-Boas' side next season. Given Villa's versatility too, there will be options at hand in how the coach deploys his forwards, as well in relation to others like Clint Dempsey and (hopefully for Spurs) Gareth Bale.
It is the prospect of Villa leading the Spurs attack that is most appealing. With the support of players like Bale and Aaron Lennon, it is unlikely he would be isolated too often.
Similarly, Spurs' supporting players would relish working with a striker as instinctive and positionally-honed as the Spanish star. His finishing is second to none too, and if he can reach his best levels, would be a match for any striker in the division.
It is difficult to get an accurate fix on Villas-Boas and Spurs' intentions for their attack heading into next season.
Villa might not even turn out to be a realistic proposition. He could head elsewhere, Spurs sign Damiao instead, and the younger man turns out to have been the smarter signing.
Hypothesizing to an extent it might be, but that is the kind of thinking a player like David Villa inspires. Even on the wrong side of 30, it is an exciting prospect to imagine him starring for Spurs next season.