Sharapova may carry the stigma of a positive doping test but she is also a global icon. This makes her especially valuable at a time when the absence of mother-to-be Serena Williams, as well as the possible unavailability of new mother Victoria Azarenka and knife-attack victim Petra Kvitova, could leave women's draws short of star quality.
The All England Club is likely to face the same dilemma as the FFT - unless Sharapova takes the matter out of its hands by gathering 600-odd rankings points between now and the end of the Internazionali BNL D'Italia in four weeks' time, and thus earning a place in the Wimbledon main draw by right.
And if the FFT does not hand a main-draw wild card to Sharapova, the All England Club would find it difficult to grant her one without being portrayed as appeasers on the issue of doping. Tim Henman, who chairs the wild-card committee, is understood to take a strong line on this. In all probability, Sharapova will collect the 260-odd rankings points that she needs to earn over the next five weeks to win a place in Wimbledon qualification. Although there is an awkward detail here. Unlike Roland Garros, Wimbledon does not have the facilities to run qualifying on its main site.
As a result, the event is staged on the Bank of England ground in Roehampton. In normal circumstances, there are no stands, no media facilities, and the relatively small number of spectators simply walk in without charge. All that would have to change, at no little expense, were Sharapova to be involved. Still, as with the French Open, there would be countervailing benefits in profile for the event as a whole.
Back in Stuttgart, Sharapova will end her 15-month doping ban on Wednesday with a first-round match against Italy's Roberta Vinci. Following the lead set by many of the leading players, Vinci said on Monday that she did not approve of the wild cards being handed out to Sharapova. One side-effect is that Vinci's compatriot, Francesca Schiavone, is likely to miss out on a place in Rome in three weeks' time.
"I don't agree about the wild card here," Vinci explained, "and about the wild card in Rome and the other tournaments, I think she [Sharapova] is a great player, person. She made her mistakes, for sure, but she paid and she can return to play but without any wild cards, any help, but just to play.
"And, for me, probably she would play two or three tournaments and be in the top 30, for sure. I don't want to think right now about the wild cards. I'm just staying focused as I have to play against her."