This comes after present Chief Minister Manohar Parrikar is set to resign.
D'Souza said that when he joined the party, he was told by Parrikar that he will be taken care of. But now, with multiple options for the post, he's dissent and says will quit party if not chosen.
Six of the BJP's 21 Goa legislators at D'Souza's house say they support his candidacy for CM.
The Deputy chief minister is one of the front runners for the post, but his rivals are seen as stronger contenders. Both Health Minister Laxmikant Parsekar and the state's Speaker Rajendra Arlekar enjoy the backing of the Rashtriya Swayamsevak Sangh or RSS, the BJP's ideological mentor.
D'Souza clarified that he will not blame the RSS as this seems to him as the "manipulation of a few."
D'Souza insists that he should be the "obvious choice" as Deputy CM to become chief minister.
"I am a four-time MLA, three-time minister, an eligible candidate," he said, and added warningly, "If I'm not CM then I will think twice if I should be in Government."
Parrikar will resign on Saturday after a meeting of the central parliamentary board of BJP in New Delhi. A meeting of the BJP legislature party will be held here to choose his successor.
"The BJP parliamentary board would be meeting in Delhi tomorrow morning (to decide on Parrikar's successor). After that I will resign and within two hours new chief minister would be sworn in," he told reporters after attending the crucial meeting of party legislators here this morning to discuss the names.
During the meeting, three names - state health minister Laxmikant Parsekar, Speaker Rajendra Arlekar and deputy chief minister Francis D'Souza - were shortlisted for the top post.