Ms Deacon has ruled herself out of the race
No other candidates have yet put their names forward to replace Henry McLeish and give Scotland its third first minister since the Scottish Parliament's inception.
The Labour party's Scottish Executive will meet in Stirling on Saturday to decide the timetable for the race to succeed Mr McLeish.
Mr McLeish resigned from the post on Thursday after the so-called Officegate affair over expenses at his constituency office in Glenrothes, Fife, while he was a serving MP.
Ms Deacon had been considered within Labour circles to possess the leadership credentials required to succeed as first minister.
Although no one has declared his or her intention to stand for the post, it has not stopped speculation on a likely successor.
Mr McConnell is believed to be in the running alongside the ministers for enterprise, Wendy Alexander, finance, Angus MacKay and minister for social justice, Jackie Baillie.
Possible successors are spending the weekend sounding out support and it is expected that several will announce their candidacy for leadership on Monday.
A spokeswoman for the Labour Party said Ms Deacon had decided not to run for the Scottish Labour leadership because she was expecting her second baby in the spring.
She said: "I can confirm that the story is true but I am not able to give any more details at the moment."
Ms Deacon, the MSP for Edinburgh East and Musselburgh, lives in Musselburgh with her partner, John Boothman, and their daughter, Clare, aged four.