Carrick gave a measured account of the encounter, declining to read too much into it.
"We had a chat, we had a cup of tea. Casual chat, it was nice to see him showing his support. That was it. It was quite informal but it was nice to see him. As a club, we're hugely connected all the way through. It's a big part. I'm really conscious that's how it should be and I am trying to do my part."
When asked about his future directly, Ratcliffe said only: "Not going there."
Carrick's Manchester United could secure a top-five finish this week. A win over Brentford on Monday and a Liverpool defeat elsewhere would move them to within one point of sealing Champions League qualification with four games to spare.
"It's certainly where we want to be. We've had some great nights in the competition. We're in a decent position. There is hopefully more to come and we want to keep pushing. But it just shows you how difficult it can be to live at the top."
An announcement on Carrick's future is expected within four weeks, at the end of the season.