The Finnish stopper suffered the injury during the weekend clash with Tranmere, and Allardyce was left with only second choice Steve Banks to cover, as Matt Glennon is on a season's loan to Carlisle.
Wright was immediately linked, along with Sheffield United's Alan Kelly, Bradford's Matt Clarke and Ipswich's Keith Branagan - a former Bolton star.
Allardyce has now admitted that he is interested in taking the 37-year-old to The Reebok Stadium on loan until the end of the season, with his Maine Road counterpart Joe Royle ready to discuss the move with Wright on Wednesday.
With Carlo Nash being brought in as understudy to Nicky Weaver last week, the writing was clearly on the wall for the veteran former Northern Ireland international, and he is now to be given the chance to move across Lancashire.
"Sam got in touch and has enquired about Tommy's availability," said Royle. "I have told him that I have no objection. I will be talking to Tommy."
Allardyce admitted that he would like to secure a deal for Wright, telling the official Bolton website: "If Tommy is available he would definitely fit the bill.
"He is experienced and capable and would probably be prepared to come in and fight for his place rather than others who might be looking to go straight into the team."
Click here to read our previous story, Bolton Linked To Goalkeeping Duo
Click here to read our previous story, Jaaskelainen Shocker Sparks Keeper Hunt
