In one word , WHY ? There just isn`t enough processing power with a arduino . To need a giga bit connection you will need a system with inbuilt hard drive interface , the imx6 part has problems saturating the gigabit connection , so you will have problems with a arduino saturating a 10 mb connection . So back to the question , WHY ?
so, if I wanted to use it with Udoo, it would be same story? so much you could do with 2 ethernet connections.
One of the Freescale PDF documents (i.MX6 errata sheet?) mentions that the onboard Gigabit interface maxes out at about 450Mb/s. All I/O connections exposed through a Udoo's shield headers are generally low-speed signals and buses (i2c, SPI, serial UARTs, etc.) unsuitable for connecting even a 10Mb Ethernet interface, let alone Gigabit. The one exception might be the SDHC1 interface pins, which could theoretically support SDIO, but I've never seen a wired-Ethernet SDIO interfaces, only Wifi and Bluetooth (which makes sense, considering the form-factor-- just imagine trying to mount an RJ-45 connector on such a tiny card). The i.MX6 chip has a single-lane PCIe controller, which would have been ideal for attaching a second NIC, but unfortunately this isn' t implemented on the Udoo. Like Peter said, your best bet is probably a USB 2.0 100M interface-- Gigabit would be pointless, but USB 2.0 should at least provide sufficient bandwidth for an Internet upstream connection. A kernel compile will probably be necessary to add necessary device drivers. Another option is to consider using an 802.1q VLAN-capable switch, and configure VLAN tagging to "split" the single onboard NIC into however many independent ports you need (after adding CONFIG_VLAN_8021Q support to the kernel, and installing Debian/Ubuntu 'vlan' package to get the 'vconfig' utility). This is how most of the small home/office routers from Linksys, Belkin etc. work, and is what I'll be doing with my Udoo when it takes over as my router/server/home-automation controller. The ports share bandwidth, but are otherwise fully separate for configuration & security purposes, appearing in isolated broadcast domains as eth0.1, eth0.2, etc. Some small and inexpensive 8-port switches, such as those based on the Realtek 8309SB / 8309SC chips, can be modified to support VLAN tagging by adding a preprogramed 24LC02 I2C EEPROM. Here's a page talking about that: http://debugmo.de/2010/01/manage-your-switch/ I've successfully made this modification using a US$15 Rosewill RC-406 switch (sadly no longer for sale, and the replacement RC-406X no longer uses a Realtek chip), setting it up for four VLANs-- two Internet upstreams, one wireless/DMZ port, four internal LAN ports, and one tagged "trunk" port back to the router. This has been working great for about five years. I'll post the EEPROM contents if anyone's interested. With a Udoo's I2C buses, reprogramming the VLANs on the fly should be possible too, with an additional GPIO connection to the switch chip's RESET input to force a config reload when desired. The only part that's a little tricky is soldering wires to the fine-pitch pins of that surface-mount RTL8309S_ switch IC.