Praise be to Allah
We have not come across these words that are attributed to Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him); rather it was quoted by Ibn Rajab al-Hanbali (may Allah have mercy on him) from Ibn Hubayrah. He (may Allah have mercy on him) said – quoting from Ibn Hubayrah (may Allah have mercy on him): If (the night before) Friday coincides with one of the odd-numbered nights during the last ten, then it is more likely than others (to be Laylat al-Qadr).
End quote from Lataa’if al-Ma‘aarif by Ibn Rajab (p. 203)
Perhaps the one who held this view based it on the fact that the night before Friday is the best of the nights of the week, so if it coincides with one of the odd-numbered nights in the last ten nights of Ramadan, it is more likely to be Laylat al-Qadr. But we have not come across any hadith of the Prophet (blessings and peace of Allah be upon him) or any words of the Sahaabah to support this view. What the hadiths indicate is that Laylat al-Qadr may be any of the last ten nights, and that it is more likely that one of the odd-numbered nights will be Laylat al-Qadr, and the most likely of these nights is the night of the twenty-seventh, without stating for certain that it is Laylat al-Qadr.
The Muslim should be keen to strive hard throughout the last ten nights, following the example of the Messenger of Allah (blessings and peace of Allah be upon him).
Shaykh Sulaymaan al-Maajid (may Allah have mercy on him) said: We do not know of any evidence in Islam to suggest that if the night before Friday coincides with an odd-numbered night, then it is Laylat al-Qadr. Based on that, we cannot be certain of that or believe that it is true. What is prescribed is to strive hard on all the last ten nights, for whoever does that will certainly have caught up with Laylat al-Qadr. And Allah knows best.
al-Haafiz Ibn Hajar (may Allah have mercy on him) said:
Laylat al-Qadr can only be in Ramadan, then in the last ten nights thereof, then in the odd-numbered nights, not in any particular one of them. This is what is indicated by a number of reports that were narrated concerning that.
End quote from Fath al-Baari (4/260)
An-Nawawi (may Allah have mercy on him) said:
The hadith of Ubayy ibn Ka‘b says that he used to swear that it was the night of the twenty-seventh, but this is one of several opinions concerning it. Most of the scholars are of the view that it is an unknown night among the last ten nights of Ramadan, and it is most likely to be on an odd-numbered night, and the most likely night is the night of the twenty-seventh or the twenty-third of the twenty-first, but most of them are of the view that it is a specific night that does not move. However, some scholars said that it does move, so in one year it may be the night of the twenty-seventh, and in another year it may be the night of the twenty-third, and in another year it may be the night of the twenty-first, or some other night, and this is more likely to be correct. In this way we may reconcile among the different hadiths.
End quote from Sharh Saheeh Muslim by an-Nawawi (6/43)
For more information, please see the answer to question no. 50693
And Allah knows best.