Griffths, the Welshman who starred in the club's dominant sides of the 1950s, slotted over 147 in the 1955-6 season.
Holroyd's four in the 38-28 loss to Celtic Crusaders took him out to 140, with a minimum of two National League One matches remaining.
"I know it's getting closer," said the 32 year old, who narrowly missed out on both the goals in a game and points in a game records when Fax walloped Workington Town 88-6 in the Northern Rail Cup at the Shay earlier this year.
"If I do it, I do it, but I'd rather just concentrate on winning a few games between now and the end of the year.
"It's a benchmark that's stood for a long time and it would be nice to get my name up there.
"It's a credit to the boys and the number of tries they have scored this year.
"It's my job to turn the fours into sixes and I've probably never kicked as well as I have over the last 18 months.
"If it turns out that I don't do it this year, I will have another go next season."
The chances of the former Leeds, Salford and Doncaster player doing that hinge on his ability to agree a new deal with Matt Calland's side for 2009.
Calland has snapped up several key members of his squad already, with Holroyd's name a notable omission amid a rash of recent announcements.
But the former Siddal junior confirmed talks were ongoing, with the lure of a potentially lucrative three-month testimonial - agreed by the Rugby Football League over the weekend in recognition of Holroyd's 16-season professional career - likely to add value to what he believes will be his final campaign.
"I have spoken to the club and hopfully we are at the stage now where we are finalising a few things," said Holroyd.
"I have been given a three month testimonial by the RFL for my services to the game, which is good of them.
"It's been 16 years now and to be recognised for that longevity is great for me.
"I want to have that at my hometown club so my aim is to sign for one more year and then call it a day.
"We are close to an agreement, and to be fair I do want to play here, but I also have to look after my family and make sure it's right for them too.
"But I don't want to potter around different clubs and be remembered as someone who couldn't really do much at the end.
"I have seen players do that and that's how you remember them so I will know when the time to quit comes.
"I want to go out on a high."

HALIFAX'S Supporters' Trust are offering coach travel to Featherstone for Sunday's final National League One round.
Seats are £8 for adults and £4 for children and the coach leaves the Shay at 1pm.
Further details are available from Neil Arber on 077144 88080.