Owner Behdad Eghbali said Chelsea would “tweak” their model and add experience to what he still believes is a strong core of young players, including Cole Palmer, Moises Caicedo and Levi Colwill.
Welbeck joining Chelsea would be another sign of a shift in strategy.
Their move for him follows attempts to sign 33-year-old midfielder Granit Xhaka from Sunderland, with the Black Cats refusing to sell the Switzerland captain.
Although the arrival of Rogers, 23, fits the club’s preferred policy of signing younger players, he brings significant Premier League experience.
The Blues are also expected to complete a £52m move for Lacroix, 26 – further Premier League-ready experience.
It is clear that Welbeck’s arrival would leave Chelsea with an abundance of attacking options for a season when they are not involved in European competition so do not necessarily need such resources.
At his age, Welbeck may be content to provide cover for Joao Pedro, but the move would represent bad news for several other forwards.
Nicolas Jackson is open to leaving, while Delap and Emmanuel Emegha had hoped to establish themselves under Alonso.
Nevertheless, the Chelsea manager is getting what he wants: experience and strong personalities to address shortcomings that contributed to the team’s 10th-place finish in the Premier League last season.
Additional reporting by Matt Jones