The 34-year old forward is currently a free agent, having left Brazilian club Atletico Mineiro, and he has been sent an offer by the Conference South side.
Whilst it is unlikely that the modern day legend will be willing to sign for the Dragons, the club have admitted that they are not using the offer as a publicity stunt, and are hoping that that the World Cup winner will be tempted by a move - even if just for one game.
Speaking to Goal.com, the club’s marketing director Simon Hood revealed the reasons for the decision, which mostly amount to a refusal to accept the impossible.
He said: “We looked at the free transfer list last week and thought ‘wow, why not give it a go?' You never know, anything’s possible in football I suppose, especially in the luck we had with the stadium being named the Soccer AM Stadium earlier this year.
"It is publicity as well of course, speaking from the marketing side, but we sent an offer to his agent.
"We haven’t heard anything back, obviously I don’t expect us to. But I imagine, even for one game, we would sell out the attendance and the shirts would sell out, it’d be huge commercially for the club.”
In keeping with their non-league standing, the club would only be willing to offer the two-time FIFA World Player of the Year wages in line with the rest of their playing squad.
“We’ve put an offer together and sent it over. Speaking to our manager, the way our club works is that everyone is on the same kind of salary so we wouldn’t break records, we’d keep everyone on the same level.
“That’s the way we work as a club. We wouldn’t increase it, we’re a non-league football club, we wouldn’t be able to afford it and for us to spend a large sum of money on one player, it wouldn’t be the right decision for the club.”
If Ronaldinho is to move into English non-league football, he would join a select list of famous players who have done the same - with the most famous being fellow compatriot Socrates. The former Selecao captain turned out for Garforth Town in the winter of 2004, playing 12 minutes of non-league football whilst signed to a one-month player-coach contract.
Basingstoke are waiting to hear back from the highly decorated player, who has won the UEFA Champions League, the FIFA World Cup, the Copa America and league titles in Spain, Italy and Brazil throughout his illustrious career.