Woodgate is out of contract this summer and, at 35, the experienced centre-half had already contemplated retiring earlier in the season.
However, Karanka is granting him the luxury of choosing his own path - whether that be staying on at Rockliffe or leaving football behind completely.
"With Woody, I have to speak with him and the club," said Karanka.
"I've always said that he can do whatever he wants here because he's a Middlesbrough man, and I'm going to help him with whatever he wants.
"If he wants to keep playing, then I'll try to convince the club or if he wants to join us as a member of staff I'm going to help him, because I think for the future of Middlesbrough Football Club Woody can be a good person here."
Should Woodgate choose to hang up his boots, Karanka will be left even more sort of cover at centre-back after Kenneth Omeruo and Fernando Amorebieta both returned to their parent clubs following loan spells.
Omeruo enjoyed a scintillating loan spell at the Riverside in 2013-14, but was unable to recreate that form last time around and endured a difficult time on Teesside.
Despite Omeruo playing second fiddle to Ben Gibson and Dani Ayala for most of the season, the Head Coach still heaped praise on the Nigerian international.
"Ken couldn't play this season in the same way that he played last season, but he's an amazing kid," said Karanka.
"He deserves all the best but I prefer to not say anything about players and their futures, because I need to think."