The branch of her conservative Moderates in Stockholm has just given her its backing.
Even though not everyone is on board - for example, Jönköping county just lent its support to Catharina Elmsäter-Svärd instead - TT reports that no other person has yet been seen as a real rival to Kinberg Batra.
Former infrastructure minister Elmsäter-Svärd has formally ruled herself out of the race.
Kinberg Batra is presently the economic and political spokesperson for the party, and also their group leader in Parliament. She has been standing in for the former prime minster Fredrik Reinfeldt at meetings, and Monday she represented the party at the joint press conference for the Alliance coalition's shadow budget.
The party will vote in early March to formally decide on a new leader.