The English central midfielder has been offered a new deal by the Fir Park club but has yet to commit.
However, Well don't want to be hanging around as they look to start their preparations for the new campaign and their Champions League qualifier.
Keith Lasley, Steve Hammell and reserve goalkeeper Lee Hollis have already agreed new deals and Black hopes Jenno will follow in their footsteps.
"At the minute there's no update with Steve, but talks are ongoing and we would hope that something will be finalised before the weekend," said Black.
"We're delighted that we have already secured three of our players on new contracts because we are well underway now with our plans for the season ahead.
"We are hoping for a positive outcome with regards to Steve, but the bottom line is that whatever decision he comes to, we really need to know what it is within the next few days.
"We don't want to be hanging around three weeks from now and wondering what is going on because there is a lot of work for us to get through between now and the start of pre-season training at the end of the month.
"If we need to go and look at other options then ideally we'd want to be doing it sooner rather than later."
Motherwell have been beneficiaries of Rangers' demise this season, with the Fir Park club taking the Ibrox side's European place.
Like Celtic, the third round qualifying tie will be Motherwell's first competitive game of the season, but Black believes they will be ready to hit the ground running.
"We are back on June 28 and we think that is ample time for us to get into gear," said Black.
"It is exciting times for us and I know everyone at the club already has their sights trained on July 20 when we find out just who we will get.
"It is an amazing opportunity for us and one that I think we'll be ready to take."
And the Fir Park assistant also believes that bad boy Chris Humphrey will be quick to learn his lesson this week.
The Well winger was booted out of the Jamaican squad after breaking a curfew and is now banned for two games against Guatemala and Antigua.
However, Black is sure the 24-year-old will be quick to toe the line and he doesn't expect that it will spell the end of his 2014 World Cup aspirations.
He said: "The one thing I would say is that this is totally out of character for Chris. I am reluctant to speak too much about it because I haven't spoken to the lad himself.
"He finished the season pretty strongly for us and I would imagine that this is down to a misunderstanding. I'm certain he will be quick to learn from it."