The Australian contractor, which is due to build the £410m Wembley stadium, is up against Bovis Lend Lease and Laing O'Rourke for the Richard Rogers-designed scheme.
The project team was informed of Multiplex's bid last week. A project insider said: "It was quite a shock."
Building revealed last month that Laing O'Rourke was teaming up with Mace to bid the job. Mace, which is also the scheme's project manager, is giving preconstruction advice to the contractor.
Carillion, Sir Robert McAlpine and Skanska dropped out of the two-stage tender process earlier this year.
The project would be the first big London scheme to be undertaken by Laing O'Rourke, which began trading in March after O'Rourke's acquisition of Laing Construction last year for £1.
Insiders said last month that competition was neck-and-neck between Bovis Lend Lease and Laing O'Rourke/Mace. One said: "They both have first-class teams. It would come down to the toss of a coin to choose between them."
Multiplex's intervention is the latest twist in the Paddington story. The scheme was radically redesigned after the Royal Parks Agency and English Heritage said Rogers' original design was visually intrusive.
Chelsfield responded by reducing the height of the towers by 12 storeys from 30. The scheme, which forms part of the Paddington Basin regeneration project, now includes six interlinked blocks of nine, 12, 15, 18, 24 and 30 storeys.
A revised planning application for the project was submitted by Chelsfield in November.