The Trotters boss is keen to strengthen his defensive hand and free agent Onopko, who is captain of Russia and Swedish international Mjallby of Glasgow Celtic are two of the people on his shortlist as the deadline looms closer.
Everton had offered Onopko a trial last week but decided not to further their interest in the player, Allardyce confirmed they where prepared to offer a better deal than Wanderers for the 34-year old veteran.
"We made Onopko an offer a while back but Everton came up with more money. I'll look into what went on to see if we can ressurect a deal" he told the clubs official site.
Mjallby on the other hand is another player of particular interest to the Trotters however the players injury problems would be a massive factor on whether or not the 32-year old Swede moves South of the border.
"There would be issues over his injury problems and the medical people would have the final say on whether we could take him" he added