Dubliner Kendrick is one of five players from last season's squad at Drogheda who have been on trial with the club in Baku.
And Drogheda's Australian-born defender John Tambouras, who has previously played in exotic spots like Greece, Malaysia and New Zealand as well as his native Australia, has already signed a deal with Neftchi.
Neftchi's German-born coach also likes the look of Kendrick, who has been offered a lucrative deal by the club, but the 25-year-old says that he will take his time before making any move.
"I went there on trial, I did well and they have offered me a very good deal; they want me to sign," he said.
"I will take a few weeks to think it over as it would be a very big move to go out there, and I would prefer to stay with Drogheda if at all possible.
"I only moved back to Ireland this year after a long while in England, and I would like to stay.
"We're all waiting to see if Drogheda can survive and what sort of club it will be next season. If they do survive and can keep us on I'd love to stay.
"I am living in Drogheda, I have seen around the town the efforts that the fans and the people of Drogheda are making to keep the club going, so it would be great to see Drogheda United survive.
"But I have to think of my career as well, so Baku is an option. I will think about the offer over Christmas and go back to them in the new year," added the former Under-21 cap.
Kendrick was a trainee at Newcastle United and also spent one season with Bundesliga side 1860 Munich before spells in England with Darlington, Workington and Tamworth.