The Blues were beaten by goals from Conor Shaughnessy and Colby Bishop on a frustrating night at Fratton Park, which came on the same day that McKenna was linked with a move to the Vitality Stadium.
The rumours come following the news that Andoni Iraola will be leaving the Cherries this summer. Rayo Vallecano's Inigo Perez, Coventry City boss Frank Lampard and former Borussia Dortmund manager Marco Rose have been among those tipped to replace him, with many outlets and bookmakers also putting McKenna's name in the picture.
Andoni Iraola will leave the Cherries at the end of the season (Image: PA)
The i have gone as far as reporting that the Northern Irishman would be keen on taking over at Bournemouth, seeing it as 'the next logical step' for him.
Asked about the links this evening, McKenna replied: "No, nothing to say on that. I've got no interest in discussing or thinking about that at the moment.
"It's such an important time for us here and just full focus on our goals.
A follow-up question was asked about McKenna's knowledge of the rumours, to which he responded: "Focus is just on such an important stage of the season with us right here."