The Guardian says both men have been informed that they are in the running to replace Mark Hughes as the Rovers chairman John Williams attempts to fill the vacant manager's position within a week.
Shearer is strongly favoured to make his first step into management at Ewood Park, with the former coach Tony Parkes among those championing his cause, though he and Allardyce are not the only options. The MK Dons manager Paul Ince is also under consideration while Steve McClaren, Henk ten Cate, despite being in negotiations with Panathinaikos, Dick Advocaat and the former Rovers' defender Henning Berg, now coach of Lyn Oslo, have all been discussed at boardroom level.
"The work we've put in has resulted in a shortlist of very exciting candidates," Williams said. "It's important after Graeme Souness and Mark Hughes that we now make it three successful appointments in a row. "