With Juventus thought to be waiting in the wings to lure Benitez to Italy, the disclosure that the Spaniard has twice in the past two weeks cancelled scheduled meetings with chairman Martin Broughton has fuelled yet more speculation that he is poised to quit Anfield.
'There is a breakdown of communications between both parties which suggests a parting of the ways is becoming a possibility,' reports The Daily Mirror.
'And if that happens, Dalglish looks likely to step into the breach on a temporary basis, with fellow Liverpool legend Ian Rush, to provide stability and breathing space in the search for a permanent successor.'
That search, however, may have to be shelved until the identity - and financial prowess - of the club's new owners is confirmed.
'Until the identity of the prospective investors is known, the club has no real idea of the package they can offer to any managerial candidate. It would leave them in limbo, but Dalglish is prepared to offer his services to the club he still passionately supports, to ensure that an experienced hand is at the rudder, during the planning stage of the summer months.
'Dalglish though, has no desire to take the position on a permanent basis, and he will cover temporarily, in the belief that the takeover issue can be resolved sufficiently to attract a top class manager.'