Jones is contracted until next summer and Twickenham's initial eagerness to extend the head coach's tenure in the wake of last autumn's march to the World Cup final appears to have cooled.
England signed off a Six Nations campaign truncated by the coronavirus-enforced postponement of their final match against Italy with a 33-30 victory over Wales at Twickenham that completed a first Triple Crown since 2016.
When asked if he will still be in the post beyond 2021 Jones replied "I don't know", but did reveal that a meeting with Sweeney is planned.
"We've got dinner organised in a couple of weeks so we may be able to chat about it. It must be his shout. I'll take a Triple Crown to show him," he said.
On the eve of the Six Nations, Jones stated that he would stay for as long as he felt the players were responding to his methods but after Wales were seen off he would only say "I'm still judging. I'll judge for as long as I need to".
Jones hinted at the toll taken by the Six Nations by reflecting on the lack of joy he gets from his role.
"I never enjoy coaching. Winning is a relief. Anyone who tells you they enjoy coaching is lying," Jones said.
"All you do is coach hard. If you win you feel good for 24 hours and then you're back into it. That's all it is.
"It's a choice you make. You get to coach these extraordinary, gifted players. You give them something that helps develop them as a player and a person.
"The joy you get from that is unbelievable, but generally any coach who says they find coaching enjoyable is probably not telling the truth."
Were it not for a defeat to France in the opener, for which Jones takes responsibility for physically under preparing his team, England would stand one win away from the Grand Slam.
Victory over Scotland at Murrayfield in atrocious conditions, a rout of Ireland and roller-coaster win against Wales placed them back in the title mix, but the championship has been a water-treading exercise that has failed to build on the World Cup.
"I haven't got any regrets over France. What I do know is that we are in a position where we can win the championship and that's where I want to be," Jones said.
"I just think you can't put a figure on it but I think the team is growing, we have that feeling that we are growing.
"We played a tough game against Wales, we played some brilliant rugby against Ireland last week, played some sensible rugby against Scotland after what was a disappointing game against France.
"And that was 100 per cent my fault for the preparation we gave the players. I'm really pleased with the way we finished the tournament."