IIRC, in the light novel, Saori never confessed to Kyousuke, nor in the anime. Saori did insisted that she's the best to take care of Kyousuke like you mentioned. But this seems more like she did that so that she stays true to her Saori Bajeena character, rather than a real romantic feelings towards Kyousuke.
The possible reason for this is that at that time, all the other girls insisted on taking care of Kyousuke. It fits Saori Bajeena's cheerful persona more if she were to also join the fray rather than staying quiet.
Another possibility for her behavior was that at that time there were Kuroneko and Kanako competing for the position. Saori surely knows who they are to Kirino. Were Kirino to choose either one, the other is surely to be hurt. Saori proposed herself so that Kirino won't be troubled choosing between the two (three if you count Manami, but Kirino won't choose her anyway).
It should be noted that in the end Kirino chose Ayase instead of Saori. Possibly because Kiririn felt that Saori is also attracted to Kyousuke. This is not likely though, since Ayase actually has a feeling towards Kyousuke and she still chose her.
Source: I read the novel.