The move cannot be ratified until the Shrimpers have their transfer embargo lifted by the Football League.
Southend chairman Ron Martin has told BBC Essex he is confident of being able to register players by Wednesday.
Simpson joined Posh from Histon in November and went on to score two goals in 21 Championship games.
The club have arranged pre-contracts with 14 players as boss Paul Sturrock looks to completely rebuild his side.
Source: BBC Sport
Source: BBC Sport