Look here, page 317 first column they show the Horizontal Parallax correction for the sun. ZERO - there is no correction due to the distance of the Sun from Earth [link to www.irbs.com]

You would have to look in the Nautical Almanac to get the correction for the planets, but it would be USELESS because the change would be extremely SMALL!!!

Page 319, they show the Horizontal Parallax correction to the Moon, it equates to a correction of 4.0' which is 4 nautical miles on earth.
2007. Reducing A Moon Sight
The moon is easy to identify and is often visible during the
day. However, the moon’s proximity to the earth requires applying
additional corrections to ha to obtain ho. This section
will cover moon sight reduction.
At 10-00-00 GMT, June 16, 1994, the navigator obtains a
sight of the moon’s upper limb. Hs is 26° 06.7'. Height of eye
is 18 feet; there is no index error. Determine ho, the moon’s
GHA, and the moon’s declination. See Figure 2007.
Body Moon (UL)
Index Correction 0.0'
Dip (18 feet) -4.1'
Sum -4.1'
Sextant Altitude (hs) 26° 06.7'
Apparent Altitude (ha) 26° 02.6'
Altitude Correction +60.5'
Additional Correction 0.0'
Horizontal Parallax (58.4) +4.0'
Moon Upper Limb Correction -30.0'
Correction to ha +34.5'
Observed Altitude (ho) 26° 37.1'