Former Red Rose all-rounder Glen Chapple replaced Ashley Giles as head coach at Old Trafford last week.
However, the club are exploring adding options in the shortest format.
"Glen is the head coach but we may find ourselves in a position where we want to look at the possibility of an iconic player or coach for T20 cricket," Allott told BBC Radio Lancashire.
Australia all-rounder James Faulkner and South Africa all-rounder Ryan McLaren have already agreed deals with the club to play in this summer's T20 competition, so any major signing would have to be a coach or non-overseas player.
Former England fast bowler Allott, 60, said they may also add more experience to their squad before the County Championship campaign gets under way on 7 April.
The Division One side will be without South African batsman Alviro Petersen, who is banned for attempting to cover up match fixing, and New Zealand paceman Neil Wagner who has joined Essex.
Opener Haseeb Hameed, wicketkeeper Jos Buttler and seamer James Anderson also look set to spend time with England in the summer.
"It's pretty obvious when you look at our squad we have lost players," Allott added.
"It stands to reason we need some senior experience. It may well be we sign a senior player or two very shortly."
Allott also added they could appoint a director of cricket to work alongside Chapple in the future.
Lancashire board member and ex-bowler Paul Allott says the county may look to sign a big name for the 2017 T20 Blast.