Speaking at the Geneva motor show, Bigland said the Giulietta and Mito would "stay for the foreseeable future", but new Alfas would be like the Giulia and Stelvio and "put the driver at the centre", in line with the firm's new strategy.
"They are very good cars but not at the same level as the Giulia and Stelvio," he said.
Bigland said that decisions on future Alfas would be taken on their global appeal above all else, and the Mito and Giulietta were very Europe-focused models.
"I have nothing to announce on this, but our lens will be less Europe and more the entire globe. The European market will be a consideration, but we'll take quite strongly Asia and North America [into consideration too]. In China and North America, the compact segments are small segments [for sales]."
To that end, Bigland said the next Alfa model would most likely be an SUV, sized immediately above or immediately below the Stelvio. He said the decision to launch future Alfas would be taken purely on the basis of the size of the global segment in which it would compete.
The biggest two global segments for premium cars is now served by the Giulia and Stelvio for Alfa, but there is debate on what size of SUV makes up the third most popular segment. That's why no decision has been taken on whether to go bigger or smaller than the Stelvio next.
The promise of six new Alfas had "slipped a little bit", said Bigland, who didn't confirm any new targets.