The club have offered a new two-year deal to Brooks, 34, who has been offered a three-year contract by Somerset.
Yorkshire see Duckett, 23, as the ideal man to boost a batting department that has struggled for consistency in the County Championship.
In addition, The Yorkshire Post understands that Yorkshire captain Steve Patterson and all-rounder Tim Bresnan are poised to commit their futures to the club, while talks have begun with Adil Rashid’s agent with a view to keeping the England leg-spinner at Emerald Headingley.
However, it is believed that opening batsman Alex Lees could soon follow England all-rounder Liam Plunkett to pastures new, with Plunkett having recently agreed a three-year deal with Surrey.
Martyn Moxon, the Yorkshire director of cricket, confirmed that the club are talking to Northants left-hander Duckett, who played the last of his four Tests and three one-day internationals in late 2016.
Moxon added that further signings could be in the pipeline, and, although he did not specifically state in which areas, it is likely that the batting and spin bowling departments could be the focus of attention.
High on Moxon’s priority list is keeping Brooks, an outstanding servant since joining from Northants at the end of 2012.
Brooks has taken 290 first-class wickets for Yorkshire at 26.38 and was their leading wicket-taker in the Championship-winning campaigns of 2014 and 2015.
“It’s down to Jack to decide where his future lies and we hope that he’s going to stay with us,” said Moxon.
“He’s been great for the club – he’s a great character and is well-liked both within the dressing room and by our members – and we’ve made him the best offer that we can given everything else that we’re trying to do within our budget, and hopefully he’ll accept it.
“I think our offer is very good, but he’s got an extra year guaranteed at Somerset and what we’ve said is that we would review the situation mid-season next year with regards to the future, so there would be the potential for an extension.
“We’re just saying that we don’t want to go beyond two years at this stage, but, if he stays and is still performing, a bit like Ryan Sidebottom was, then he can definitely carry on.”
Moxon said there was no timescale on the situation, although the club are exploring their options should Brooks elect to leave.
It is understood that Somerset’s offer is a good one, and that Brooks – whose loyalty and commitment to Yorkshire cannot be questioned – is naturally weighing the pros and cons.
As for Duckett, he is a talented wicketkeeper as well as a batsman, but Yorkshire are highly satisfied with 23-year-old Jonny Tattersall behind the stumps.
As such, Duckett would perhaps be the wicketkeeping back-up to Tattersall in any move north that could help to energise his career.
“Our batting is an area that we want to strengthen, and Ben is someone that we’ve been talking to,” said Moxon.
“A few lads in our dressing room know him and have been on tour with him, and he’s very keen to resurrect his international career.
“Potentially a change of environment for him would re-start his attempt to get back into the selectors’ minds.
“We’re hopeful that we can get the deal done, but, until it is, you can never be sure.”
With uncertainty regarding Rashid’s short and long-term future, Yorkshire are adopting a watching brief as regards trying to extend the loan of Warwickshire leg-spinner Josh Poysden.
Poysden played in the recent Championship Roses match with a view to a potential extended loan/permanent move, but Rashid’s return to the Test side – for now at least – and the furore surrounding his red-ball future has made the situation fluid. “We’ve spoken to Rash’s agent and talked about what the future holds, but, understandably, Rash has been focusing on the Test match,” said Moxon. “We will try and pursue it over the next week or so, and, as each Test match goes by, things will become a little bit clearer as to what his position is with the England Test team.
“He’s England’s best white-ball spinner, and we want to keep him. As far as red-ball is concerned, things are more uncertain, and we have to try and arrange a deal whereby we’re not exposed by his potential non-availability in red-ball cricket going forward.”