Kinnear was named the interim Newcastle boss on 26 September following Kevin Keegan's exit.
But Shearer, who scored 206 goals in 404 appearances, has been consistently linked with taking the job on a permanent basis - with Keegan, another Geordie idol, also tipped for a return.
However, Kinnear said he was not worried by the speculation.
"I have just got on with things," he said.
"They are two idols that everybody loves up here, so I'm never going to be as popular as those two and I'm not trying to be. I am aware of the situation and can handle it."
In the meantime, the current Newcastle boss is busy considering player recruitment.
SCORED AGAINST NEWCASTLE
Wondering who Kinnear might be keen to sign? Take your pick: Darren Fletcher, Clinton Morrison, Scott Dann, Denilson, Robin van Persie, Marlon King, David Di Michele, Matthew Etherington, Roman Pavlyuchenko, Jamie O'Hara, Chris Samba, Roque Santa Cruz, Mikel Arteta, Marouane Fellaini, Djibril Cissť, Kieran Richardson, Robinho, Stephen Ireland, Ishmael Miller, Andy Johnson, Danny Murphy, Ryan Taylor, Titus Bramble
"We need two players in as soon as possible, and I have them in mind," he said.
"One is with Roma and isn't in the team at the moment. The other has already scored against us this season."
Following Kinnear's substantial clue about a Roma player, one man who has been heavily linked is John Arne Riise.
The 28-year-old Norwegian former Liverpool star left Anfield for Roma over the summer but having played regularly, he may not be on Newcastle's wanted list.
By contrast, French defender Philippe Mexes has made fewer appearances and was recently reported to be in talks with AC Milan, as Roma try to offload star players to service their debts.
Kinnear's other clue, about a player who has scored against Newcastle this season, does little to narrow down the list of possibilities.
It has been suggested that Arsenal's 20-year-old midfielder Denilson is Kinnear's target as he scored in the Gunners' 3-0 win earlier this season, but 23 players have scored against Newcastle this term.
Kinnear had initially expected to be in charge at the Tyneside club for a matter of weeks but, with the news that talks with owner Ashley will no longer take place after Saturday's game against Chelsea, has settled in for a longer haul.
"I have already got my shortlist ready and I will be giving it to Mike," said the 61-year-old.
"I know their agents and what they would be is loan deals from January until the end of the season. I already know the player in Rome would cost us £2m to bring over here.
"We need to strengthen the team and the squad and, if we can get them, they would be a big boost because both are top-class players."
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