The 31-year-old was one of four players recently transfer-listed by Rotherham United after they won promotion to League One.
"It was a tough decision but as ever it was very well thought through," said Millers boss.
"They'll attract interest and since we announced it we've already had people calling us about them.
"If they're still here at the end of June then we will treat them with the utmost respect."
Odejayi is not renowned as a prolific goalscorer but the all-round benefits a striker can bring to his team is normally Aidy Boothroyd's first priority.
The goals were shared around the Cobblers squad in the second half of last season and the manager, as well as hoping to have Alex Nicholls back at some stage, is also hoping that Roy O'Donovan signs a new deal.