But Merseytravel denied there was any personal dispute between the two men.
A spokesman said there was no question of having to put any personal differences to one side, no matter what Cllr Storey said.
"This is nothing to do with personalities. Sir David Henshaw and Neil Scales meet regularly. The latest problem has been caused by the decision of the Liverpool cabinet to back a second route to Liverpool airport which flew in the face of all previous agreements."
Even if the row between Merseytravel and the council is resolved next week, the damage may already have been done.
A source at the consortium which has been strong favourite to win the Merseytram contract said the current crisis was "as serious as it gets".
"We were getting ready to submit our Best and Final Offer (BAFO) documents but our board has asked us to review the situation in the light of the council's actions. We have asked for an extension until next Friday." The Merseytravel spokesman confirmed the bidders had been given a two-week extension at their own request.
He said: "We are very concerned by the city council's actions. It could jeopardise the whole scheme."
The council is a signatory to the Local Transport Plan which has Line Two linking Liverpool city centre to Prescot and Whiston Hospital.
But Cllr Storey said the council was within its rights to challenge the route of Line Two - even at this stage.
He said: "We think the better route would be to the airport as most people do and it was perfectly right for us to start that discussion.
"If it is not possible, then Merseytravel should have said so, but I have not heard from them."
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