The 31-year-old has made a big impact since joining the back-to-back Super League champions from North Queensland Cowboys in 2019 but his three-year contract runs out at the end of the season and he is weighing up whether to take his young family back to Australia.
“We’d very much love Lachlan to stay,” said Woolf, who says the Covid-19 situation in the UK will have a bearing on the player’s next move.
“He’s been a big part of this club for two years now, going into his third year, and I don’t think it’s any coincidence that the club has had success in that time.
“He’s a very good character and a very good influence on everyone at the club. And he’s obviously a very fine performer in terms of what he does on the field.
“It’s up to Lachlan to talk about the things he needs to weigh up but everyone needs to understand it’s been a difficult 12 to 18 months for everybody and in particular for people who are a long way from home. That certainly comes into the equation.
“We’re certainly hopeful that he’ll stay and I think Lachlan will tell you the same thing but we need to allow that to run its course and Lachlan will be given time because he’s a bloke that we really respect.”
Coote is expected to be available for Scotland in the end-of-season World Cup.