Kinnear vowed to implement the club's recruitment plans swiftly after holding talks with Pardew and chief scout Graham Carr following his appointment last month.
However, the Magpies went into Tuesday night's 1-1 friendly draw with Pacos de Ferreira in Portugal without a new signing on board and with Shane Ferguson following Steve Harper, Danny Simpson and James Perch out of the club, having signed a season-long loan deal with Birmingham.
Pardew told the Chronicle: "I'm pushing Joe to get a transfer in. I think we need a boost. We are in a situation where we want to progress now. The team is in a good place."
Pardew's main focus for the summer was always going to be his frontline, and the club's dual pursuit of Lyon's Bafetimbi Gomis and Aston Villa's Darren Bent is ongoing.
However, Papiss Cisse's position remains unclear with the striker still in dispute with the club over wearing the name of sponsor Wonga on his shirt and training kit on religious grounds, although his case has not been helped by pictures purporting to show him at a city casino.
The Senegal international has enlisted the help of the Professional Footballers' Association in his efforts to find a solution but there has so far been little tangible progress.
Shola Ameobi scored Newcastle's equaliser against the Portuguese amid rumours he could leave this summer, although given his lack of strength in depth, Pardew is reluctant to allow that to happen.
The pre-season fixture was marred by the sending-offs late in the first half of Magpies skipper Fabricio Coloccini and home forward Caetano but Pardew said: "Shola is a player that is under contract here. He's not made any noises to me that he wants to leave.
"Certainly with my striker situation at the moment, I need as many as I can get."