The 32-year-old striker labelled his partnership with the New Zealander as the most successful of his career.
The pair's alliance was born on November 20th, 2010, when Wood netted from the spot on his Brighton debut in a 2-2 draw with Bristol Rovers in League One.
They scored 26 goals between them that season as they fired the Seagulls to the Championship after beating Southampton to the title.
Wood, however, was only on loan from West Bromwich Albion and so the pair's promising on-field relationship was ripped apart.
But they would be reunited in 2017 when the Kiwi joined the Clarets from Leeds United as a £15m club record signing.
Barnes has 42 Premier League goals for Burnley ahead of his 200th appearance at this level on Sunday while Wood is the Clarets' all-time leading scorer in the PL with 49 goals.
The out-of-contract forward, who has a 12-month option on his contract in the club's favour, said: "With Woody, definitely. We played together at Brighton, but he was only young then.
"He has to be my number one partnership for sure, especially with what we achieved together. We worked so well, we always knew where the other person would be at all times, and where we were running. We'll make sure the lads kick him a little bit more!"
The ex-Plymouth Argyle frontman, the joker of the pack, also had a jovial swipe at Trippier before applauding the England international's success.
The right back, who made 170 league appearances for Burnley, went on to win La Liga with Atletico Madrid, scored in a World Cup semi-final for the Three Lions and then featured in the nation's first major tournament final since 1966.
"I'm still in touch with them and it'll be nice to see their faces again," Barnes said. "Tripps text me for some tickets; I don't know why he can't buy them himself! I'm going to stitch him up. We were always ducking and diving.
"What a career this guy [Trippier] has had. To leave the country and win a league is difficult. It's been amazing for him. They did an amazing job when they were here and they had a positive impact season after season."
After accumulating just one win in 21 games this season the Clarets had been well and truly written off, with most expecting the club to suffer the same fate as in 2014-15, which Barnes and Trippier were both involved in.
An 11-point return from seven games under interim boss Mike Jackson, though, has swung the pendulum back in the favour of Burnley, who need to match Leeds United's result away at Brentford to guarantee their safety.
With the two rivals heading into "Survival Sunday" locked on the same points, with the Clarets holding the advantage courtesy of a far superior goal difference, Barnes said: "We had that blip when we got relegated, but we bounced back and now we've had six successive years in the Premier League.
"It's been a good achievement and this one would top it off from where we were. After just three wins we had relegation written all over us. The lads bounced back, regrouped and went again.
"Everyone has written us off and some are still probably writing us off. We've shown that we've got a good group, I'll keep reiterating that, and everyone is fighting for each other."
He added: "We've got it in our own hands at the weekend now. We've got a good, experienced group that knows how everything works, with game management in these big situations, and hopefully that'll help us get over the line this Sunday.
"As players, as soon as we cross that white line, we've got to give it our all. We have to block everything out, everything's riding on this game for survival and it's a new situation for most of us, but we've got to stay calm, remain positive and concentrate on ourselves."